{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/10_Nonlinear_intro/10_2_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 10: Nonlinear Learning and Feature Engineering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 10.2  Nonlinear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this Section we introduce the general framework of nonlinear regression via the engineering of nonlinear feature transformations, along with many examples ranging from toy datasets to classic examples from differential equations. While this sort of nonlinear feature engineering is only feasible with low dimensional datasets, by walking through these examples we flush out a number important concepts, coding principles, and jargon terms in a relatively simple environment that will be omnipresent in our discussion of nonlinear learning going forward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "chapter_10_datasets already cloned!\n",
      "chapter_10_library already cloned!\n",
      "chapter_10_images already cloned!\n"
     ]
    }
   ],
   "source": [
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone datasets\n",
    "if not Path('chapter_10_datasets').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/10_Nonlinear_intro/chapter_10_datasets\n",
    "else:\n",
    "    print('chapter_10_datasets already cloned!')\n",
    "\n",
    "# clone library subdirectory\n",
    "if not Path('chapter_10_library').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/10_Nonlinear_intro/chapter_10_library\n",
    "else:\n",
    "    print('chapter_10_library already cloned!')\n",
    "\n",
    "# clone images\n",
    "if not Path('chapter_10_images').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/10_Nonlinear_intro/chapter_10_images\n",
    "else:\n",
    "    print('chapter_10_images already cloned!')\n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_10_library') \n",
    "\n",
    "# import section helper\n",
    "import section_10_2_helpers\n",
    "\n",
    "# dataset paths\n",
    "data_path_1 = \"chapter_10_datasets/unnorm_linregress_data.csv\"\n",
    "data_path_2 = \"chapter_10_datasets/noisy_sin_subsample.csv\"\n",
    "data_path_3 = \"chapter_10_datasets/galileo_ramp_data.csv\"\n",
    "\n",
    "# image paths\n",
    "image_path_1 = \"chapter_10_images/10_1.png\"\n",
    "image_path_2 = \"chapter_10_images/Fig_1_12.png\"\n",
    "\n",
    "# standard imports\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython, copy\n",
    "from IPython.display import Image\n",
    "import autograd.numpy as np\n",
    "\n",
    "# this is needed to compensate for matplotlib notebook's tendancy to blow up images when plotted inline\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.autolayout'] = True\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Modeling principles of linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Chapter 5 we detailed the basic linear model for regression as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\mathbf{w}\\right) = w_0 + x_{1}w_1 + \\cdots + x_{N}w_N\n",
    "\\end{equation}\n",
    "\n",
    "or more compactly, denoting\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{w}=\\begin{bmatrix}\n",
    "w_{0}\\\\\n",
    "w_{1}\\\\\n",
    "w_{2}\\\\\n",
    "\\vdots\\\\\n",
    "w_{N}\n",
    "\\end{bmatrix}\\,\\,\\,\\,\\,\\,\\,\\,\\text{and}\n",
    "\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\n",
    "\\mathring{\\mathbf{x}}_{\\,}=\\begin{bmatrix}\n",
    "1 \\\\\n",
    "x_{1}\\\\\n",
    "x_{2}\\\\\n",
    "\\vdots\\\\\n",
    "x_{N}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\mathbf{w}\\right) = \\mathring{\\mathbf{x}}_{\\,}^T\\mathbf{w}^{\\,} \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a generic dataset of $P$ input-output pairs $\\left\\{\\left(\\mathbf{x}_p,y_p\\right)\\right\\}_{p=1}^{P}$ we then minimized a proper regression cost function, e.g., the Least Squares (from [Section 5.2](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_2_Least.html))\n",
    "\n",
    "\\begin{equation}\n",
    " g\\left(\\mathbf{w}\\right) = \\frac{1}{P}\\sum_{p=1}^{P} \\left(  \\mathring{\\mathbf{x}}_{p}^T \\mathbf{w}   - \\overset{\\,}{{y}}_{p}^{\\,} \\right)^2\n",
    "\\end{equation}\n",
    "\n",
    "in order to find optimal values for the parameters of our linear model (here, the vector $\\mathbf{w}$).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Modeling principles of nonlinear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily move from linear to general *nonlinear* regression, in both its principles and implementation, with few obstacles. We do this by swapping out the linear model used in Equation (1) with a nonlinear one, for instance a single nonlinear function $f$ that can be parameterized or unparameterized (e.g., tanh, a sine wave, etc.,). In the jargon of machine learning such a nonlinear function $f$ is often called a nonlinear *feature transformation*, since it transforms our original input features $\\mathbf{x}$.  Our corresponding nonlinear model then takes the form\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\Theta\\right)  = \n",
    "w_0^{\\,} + f\\left(\\mathbf{x}\\right){w}_{1}^{\\,}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we represent our set of parameters - both those potentially internal parameters of the function $f$ and those weights in the linear combination - via the set $\\Theta$.  For example, in the case $f$ is trivially the identity $f\\left(x\\right) = x$ and our model is linear our parameter set $\\Theta$ reduces to the weights of our linear combination.  As we did in the case of *linear regression*, here we could consider the ideal case - where we have knowledge of the best possible weights so that \n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x}_p,\\Theta\\right)   \\approx y_p\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and to recover our ideal weights we would follow the same logic we used in deriving our cost functions for linear regression.  For example, we could minimize the Least Squares difference between both sides of the above and over all points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed in general we could create a nonlinear model that is the weighted sum of $B$ nonlinear functions of our input as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\Theta\\right) = w_0 + f_1\\left(\\mathbf{x}\\right){w}_{1} +  f_2\\left(\\mathbf{x}\\right){w}_{2} + \\cdots + f_B\\left(\\mathbf{x}\\right)w_B\n",
    "\\end{equation}\n",
    "\n",
    "where $f_1,\\,f_2,\\,...\\,f_B$ are nonlinear parameterized or unparameterized functions - or *feature transformations* - and $w_0$ through $w_B$ (along with any additional weights internal to the nonlinear functions) are represented in the weight set $\\Theta$ and must be tuned properly.   Nonetheless the steps we take to formally employ such a model, its ideal weight values, the derivation of a Least Squares cost function, etc., are entirely similar to what we have now seen in the simpler instance of nonlinear regression (which itself does not differ from the steps taken in modeling the linear case)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(image_path_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure>\n",
    "<p>\n",
    "</p>\n",
    "<figcaption> <strong>Figure:</strong> <em> \n",
    "(left) Linear regression illustrated. Here the fit to the data is defined by the linear model $\\mathring{\\mathbf{x}}_{\\,}^T\\mathbf{w}^{\\,}$. (right) Nonlinear regression is achieved by injecting nonlinear feature transformations into our model. Here the fit to the data is a nonlinear curve defined by $\\mathring{\\mathbf{f}}_{\\,}^T\\mathbf{w}^{\\,}$.\n",
    "</em>\n",
    "</figcaption>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In analogy to the linear case as shown in equation (3), here we too can compactly denote the generic nonlinear model in equation (6) by tacking a $1$ on top of the vector of nonlinear feature transformation as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "\\mathbf{w}=\\begin{bmatrix}\n",
    "w_{0}\\\\\n",
    "w_{1}\\\\\n",
    "w_{2}\\\\\n",
    "\\vdots\\\\\n",
    "w_{B}\n",
    "\\end{bmatrix}\n",
    "\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\n",
    "\\mathring{\\mathbf{f}}_{\\,}=\\begin{bmatrix}\n",
    "1 \\\\\n",
    "f_1\\left(\\mathbf{x}\\right)\\\\\n",
    "f_2\\left(\\mathbf{x}\\right)\\\\\n",
    "\\vdots\\\\\n",
    "f_B\\left(\\mathbf{x}\\right)\n",
    "\\end{bmatrix}\n",
    "\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\n",
    "\\mathring{\\mathbf{f}}_{p}=\\begin{bmatrix}\n",
    "1 \\\\\n",
    "f_1\\left(\\mathbf{x}_p\\right)\\\\\n",
    "f_2\\left(\\mathbf{x}_p\\right)\\\\\n",
    "\\vdots\\\\\n",
    "f_B\\left(\\mathbf{x}_p\\right)\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then writing our generic nonlinear model as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\Theta\\right) = \\mathring{\\mathbf{f}}_{\\,}^T \\mathbf{w}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To tune the parameters of our general nonlinear model consisting of a linear combination of $B$ nonlinear feature transformations to a set of input / output pairs we also do precisely what we did in the linear case - we minimize a proper regression cost function over $\\Theta$ like e.g., the Least Squares\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    " g\\left(\\Theta\\right) = \\frac{1}{P}\\sum_{p=1}^{P} \\left(  \\mathring{\\mathbf{f}}_{p}^T \\mathbf{w}   - \\overset{\\,}{{y}}_{p}^{\\,} \\right)^2\n",
    "\\end{equation}\n",
    "\n",
    "which is a direct generalization of equation (4)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Feature engineering examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we determine the appropriate nonlinear feature transformations for our model, and their number $B$?  This is one of the most important challenges we face in machine learning, and is one which we will discuss extensively in the current Chapter as well as several of those to come.  Here we begin by discussing some simple instances when we can determine these items by *visualizing the data* and relying on our own pattern recognition abilities to determine the appropriate nonlinearities.  This kind of practice is referred to as nonlinear feature engineering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 1. </span> The linear case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first examine our original linear regression throug the lense of nonlinear feature engineering.   The figure below we shows a low dimensional regression dataset that looks is a clear candidate linear modeling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load data\n",
    "data = np.loadtxt(data_path_1,delimiter = ',')\n",
    "\n",
    "# load input/output data\n",
    "x = data[:-1,:]\n",
    "y = data[-1:,:] \n",
    "\n",
    "# plot dataset\n",
    "demo = section_10_2_helpers.RegressionVisualizer(data)\n",
    "demo.plot_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this data looks quite linear in nature, we would clearly employ a linear model.  In terms of feature engineering, here we employ the simple linear feature transformation\n",
    "\n",
    "\\begin{equation}\n",
    "f\\left(x\\right) = x\n",
    "\\end{equation}\n",
    "\n",
    "and in this notation our linear model is then\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(x,\\Theta\\right) = w_0 +f\\left(x\\right)w_{1\\,}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how in performing standard normalization (subtracing the mean and dividing off the standard deviation of the input) we can actually think of the normalization as being a part of the feature transformation itself, and write it formally as\n",
    "\n",
    "\\begin{equation}\n",
    "f\\left(x \\right) = \\frac{x - \\mu}{\\sigma}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\mu$ and $\\sigma$ are the mean and standard deviation of the dataset's input. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the fit provided by minimizing the Least Squares cost employing this feature transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters for our two runs of gradient descent\n",
    "w = 0.1*np.random.randn(2,1); max_its = 500; alpha_choice = 10**(-1)\n",
    "\n",
    "# the trivial linear feature transformation\n",
    "def feature_transforms(x):\n",
    "    return x\n",
    "\n",
    "# run on normalized data\n",
    "run = section_10_2_helpers.BaseSetup(x,y,feature_transforms,'least_squares',normalize = 'standard')\n",
    "run.fit(w=w,alpha_choice = alpha_choice,max_its = max_its)\n",
    "\n",
    "# pluck out best weights - those that provided lowest cost, \n",
    "# and plot resulting fit\n",
    "ind = np.argmin(run.cost_history)\n",
    "w_best = run.weight_history[ind]\n",
    "demo.plot_fit(w_best,run.model,normalizer = run.normalizer);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 2. </span> Modeling a familiar wave using a parameterized feature transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load data\n",
    "data = np.loadtxt(data_path_2,delimiter = ',')\n",
    "\n",
    "# load input/output data\n",
    "x = data[:-1,:]\n",
    "y = data[-1:,:] \n",
    "\n",
    "# plot dataset\n",
    "demo = section_10_2_helpers.RegressionVisualizer(data)\n",
    "demo.plot_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This dataset looks sinusoidal, so we can defensibly propose a `model` consisting of completely *parameterized* sinusoidal function or *feature transformation* \n",
    "\n",
    "\\begin{equation}\n",
    "f\\left(x,\\mathbf{w}\\right) = \\text{sin}\\left(w_0 + xw_1\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can then take as our model a linear combination of this nonlinear feature transformation as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(x,\\Theta\\right) = w_2 + f\\left(x,\\mathbf{w}\\right)w_{3\\,}.\n",
    "\\end{equation}\n",
    "\n",
    "This seems like it could fit the data well if its parameters were all tuned properly via e.g., minimizing the associated Least Squares cost.  Tuning these parameters via gradient descent we can produce the following fit to our original data employing the nonlinear model above, which fits quite well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the feature transformation from Example 2 \n",
    "def feature_transforms(x,w):\n",
    "    # calculate feature transform\n",
    "    f = np.sin(w[0] + np.dot(x.T,w[1:])).T\n",
    "    return f\n",
    "\n",
    "# parameters for our two runs of gradient descent\n",
    "w = np.array([0.1*np.random.randn(2,1),0.1*np.random.randn(2,1)])\n",
    "max_its = 500; alpha_choice = 10**(-1)\n",
    "\n",
    "# run on original data\n",
    "run1 = section_10_2_helpers.BaseSetup(x,y,feature_transforms,'least_squares',normalize = 'None')\n",
    "run1.fit(w=w,alpha_choice = alpha_choice,max_its=max_its)\n",
    "\n",
    "# run on normalized data\n",
    "run2 = section_10_2_helpers.BaseSetup(x,y,feature_transforms,'least_squares',normalize = 'standard')\n",
    "run2.fit(w=w,alpha_choice = alpha_choice,max_its=max_its)\n",
    "\n",
    "# pluck out best weights - those that provided lowest cost, \n",
    "# and plot resulting fit\n",
    "ind = np.argmin(run2.cost_history)\n",
    "w_best = run2.weight_history[ind]\n",
    "demo.plot_fit(w_best,run2.model,normalizer = run2.normalizer);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "With our weights fully tuned notice that  since `model` is defined *linearly* in terms of its feature transformation we can represent our transformed input $x_p \\longleftarrow f\\left(x_p,\\mathbf{w}^{\\star}\\right)$ and the correspnoding model fit $\n",
    "\\text{model}\\left(x,\\Theta^{\\star}\\right)$ in what is called the *transformed feature space*.  This is simply the space whose input is the feature transformed input $\\,f\\left(x_p,\\mathbf{w}^{\\star}\\right)$ and whose output remains as $y$.  In this space our *nonlinear* fit is a *linear* one.  In other words, with our model completely tuned if plot the points $\\left(f\\left(x_1,\\mathbf{w}^{\\star}\\right),y_1\\right),\\,\\left(f\\left(x_2,\\mathbf{w}^{\\star}\\right),y_2\\right)...,\\left(f\\left(x_P,\\mathbf{w}^{\\star}\\right),y_P\\right)$ - as we do below in the right panel - our model fits the transformed data *linearly*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This finding is true in general with nonlinear regression problems.\n",
    "\n",
    "> A properly designed feature (or set of features) provides a good nonlinear fit in the original feature space and, simultaneously, a good linear fit in the transformed feature space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot data and fit in original and feature transformed space\n",
    "demo.plot_fit_and_feature_space(w_best,run2.model,run2.feature_transforms,normalizer = run2.normalizer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally note, as with the previous example that we can - and should - employ standard normalization to scale our input here when employing gradient descent to minimize the corresponding Least Squares cost.   *Feature scaling* is equally important in the context of nonlinear regression.  Here it also helps temper the contours of any regression cost function making it considerably easier for gradient descent to minimize.  Below we show the resulting cost function history resulting from a run of gradient descent employing the original and standard normalized versions of the input.  Comparing the two plots we can see that a significantly lower cost function value was found using the standard-normalized input.  Moreover, the convergence behavior displayed by the cost function plot on the original data is actually somewhat deceiving here - it appears to converge but not to a global minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the cost function history for a given run\n",
    "static_plotter = section_10_2_helpers.StaticVisualizer()\n",
    "static_plotter.plot_cost_histories([run1.cost_history,run2.cost_history],start = 0,points = False,labels = ['original data','normalized'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 3. </span> Using an unparameterized feature transformation to model a classic physics dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In 1638 Galileo Galilei, infamous for his expulsion from the Catholic church for daring to claim that the earth orbited the sun and not the converse (as was the prevailing belief at the time) published his final book: [Discourses and Mathematical Demonstrations Relating to Two New Sciences](https://books.google.com/books?hl=en&lr=&id=8BhZAAAAYAAJ&oi=fnd&pg=PA11&ots=5pQfKe7Bby&sig=VVWwm0GtVvS9YnydNJXHU_UxBjA#v=onepage&q&f=false). In this book, written as a discourse among three men in the tradition of Aristotle, he described his experimental and philosophical evidence for the notion of uniformly accelerated physical motion. Specifically, Galileo (and others) had intuition that the acceleration of an object due to (the force we now know as) gravity is uniform in time, or in other words that the distance an object falls is directly proportional (i.e., linearly related) to the amount of time it has been traveling, squared. This relationship was empirically solidified using the following ingeniously simple experiment performed by Galileo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Repeatedly rolling a metal ball down a grooved $\\frac{1}{2}$ meter long piece of wood set at an incline as shown in the Figure below, Galileo timed how long the ball took to get $\\frac{1}{4}$,$\\frac{1}{2}$, $\\frac{2}{3}$, $\\frac{3}{4}$, and all the way down the wood ramp. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lxAVgPYjBIAdDunAjyMLEIwazrObLZUs9YhAReJTvo3+uhSTsn3fFk0IAAhCAAAQgAAEIQAACEIAABCAAgc8loHThRuVmiBAMUrCx4+nCpZA2XPfteVTg516CnUNKAEk4pC+ebkMAAhCAAAQgAAEIQAACEIAABCDQXwQyLxhiHhWYeKpw2iyF4iGpC8BW5oVEPApQ21teSCTLfFzBED3oKcK+HoqR7EcW9lePedpOEkASdpI294IABCAAAQhAAAIQgAAEIAABCEAAAvckkBcUySsMawxAjQXoRULCZlUXbrgAbHpUoAqK7LgYzKMEQ9VhH0+w4duJFLwnXHbchwCS8D6A2A0BCEAAAhCAAAQgAAEIQAACEIAABDpBIEt8XMDEIwK9onBeVGTbmrVV31b1bSo0oqIiqiyscQbz6sS+sP9ouWDsxHNyj8EkgCQczPdKryAAAQhAAAIQgAAEIAABCEAAAhDoMQItTwNu1jZDmnBIEW6WLfNKw0myF7b7Soge1D5FEYYqw76sQiKZ78ujBKMU7LHO8Th9TwBJ2PevkA5AAAIQgAAEIAABCEAAAhCAAAQg0H0CubzLx/+T4PNU4ZAurLRhRfm56PPqwkltw8cOLIXllgqKuChMm7tWr676MQjA7r/H4X0CJOHwvnt6DgEIQAACEIAABCAAAQhAAAIQgMAREVBREUX+NauSgNthylRgxKMHU08fbjR8vMAsTxXWGINuBMN/4fZBIiIIj+hVcJmHJIAkfEhwnAYBCEAAAhCAAAQgAAEIQAACEIDA8BAIKcASfmktVAzOfJzAtLnnrs8rCyd1DxTU9tT3K4W4lo8f6JGDShPOwv4qkYLD83Hpy54iCfvytfHQEIAABCAAAQhAAAIQgAAEIAABCBw9AaUI5xF9ivNTtF8+y1wEVixr+viBze0gBVOvJNyorrkM9G1eVCT1oiJKKaZBoF8JIAn79c3x3BCAAAQgAAEIQAACEIAABCAAAQgcGYGWR/1J+qWeIpylHjHYLLkM3HMpWLJGReMFukCMVYVVVMSXPx1z0OUg2cJH9i64UHcIIAm7w527QgACEIAABCAAAQhAAAIQgAAEINAxAhJ8rvX2xw1shSrCqhbs8YJa9jTizKckVB4ue0Cg0opVUMSjB10Ups2dcGzHHpcbQaALBJCEXYDOLSEAAQhAAAIQgAAEIAABCEAAAhDoHIEsdRHoYwfmRUU2XQZueYTgjstArzZc37GGVxwmVbhz74M79SYBJGFvvheeCgIQgAAEIAABCEAAAhCAAAQgAIFDEshUIMTHBFQhES2njZI165tBAqZNLyTi+1RUREVEQgESF4atLE8XVkViXznknTgMAoNLAEk4uO+WnkEAAhCAAAQgAAEIQAACEIAABAaEQOair+HRgLnQk+DLl138eVXhOCUuCUOqsI8rmHhhkSyruTD0tGE/l0jBAfko0I1jI4AkPDa0XBgCEIAABCAAAQhAAAIQgAAEIACBoyAgQdio3AypwSFqsLFjSeKFRVwG1so3iAQ8CshcY+gJIAmH/iMAAAhAAAIQgAAEIAABCEAAAhCAQPcIqJiIeYRg4sIvVBT2aMDUBaDSghUFqO0qLqLCInn04H6xkZYqCmsiVbh7b487DxIBJOEgvU36AgEIQAACEIAABCAAAQhAAAIQ6DkCLRd5LvYk9LzCcCtIPck9bU5DenDmQlDpwSoiku5HCaqoiMYWbPh2RGDPvVQeaAAJIAkH8KXSJQhAAAIQgAAEIAABCEAAAhCAQK8QyBIfFzDxiMD6dhg7UPNmbdW3VX3brm/zoiJBIGqcQTeHuT3cf/xcMPZKX3gOCAwyASThIL9d+gYBCEAAAhCAAAQgAAEIDCSBzIs21Gp129hYt2q1apVKxW7evGn1ej30V6JldHTUlpeXbWJiwmZmZuzcuXM2Pj5uxWJxIJnQqe4RUApw2vAUYS8gEiIDk7oH/nkUoE9ZvZSnCfuYgqkXEQlpwy4HJQ09tzg/x1OJzUgZ7t4b5M4QyAkgCfkkQAACEIAABCAAAQhAAAIQ6CMCzWbTNG1v79j7779vOzs7trm5ab/97W9td9fHbgtpnbkk/MIXvmBzc3N28uTJIAclC7UuWTgyMtJHveZRu0/g3lF+ihRsVtfC2IGZi8GWRwcmiUvDZslqFRUVUXQgDQIQ6HUCI/4DhP+39vpb4vkgAAEIQAACEIAABCAAAQg4AcnBf/qnf7L19XX7+OOPQ7SgZJ+iBms1T+lMU4/aysJxWo5Rg1rWMbOzs/bUU0/Zt7/9bTt9+jRMIXBfAqoqrKIizdpWGCuw2dyxzOWftqfN3bA9RA8qXVhjDSo7eMTnmVSDi8UQJXjf23DAgBAoFBfswvM/spHCxID0aLi6QSThcL1vegsBCEAAAhCAAAQgAAEI9CkBpRNfv37drl27FtKLC4WCTU1NBfk3NjYWliUIk8SFjsvEOJcg1KSU5JiOvLCwYGfPnrUXXnjBdB3a8BJQBeGWVw0OqcKqIKxUYK8ubC1PBVbasFKIM32Gyr6vlo8f6AVFsnCspxSnFT+W2KPh/QTR80EigCQcpLdJXyAAAQhAAAIQgAAEIACBgSTQaDSCHPz1r3/tacbbQeydOXMmjDcoyadoQolByUAdq0nrii7UXAlkURaurKzYa6+9Zjr/8ccfD3IRUTiQH5u2TinCLxd5XlvYt/sUZpmLwIpHBlYsaW4HKZh6JeGGpw5nLv9UVCT1oiJuCtuuxSIEIDCoBJCEg/pm6RcEIAABCEAAAhCAAAQg0PcEFBko4feP//iPtrq6auVy2S5cuBDE3okTJ0IUoTqpqMGYbqxCJooY1HmSf9oXRaKWtf/GjRte9GTDfvzjH9uXvvQle+mllw6u1ffQ6MBnCLQ86k/SL22oirBShEsuA328QC8cUi/fdAGogiH74w36cksFRMI214khhfgzl2MFAhAYYAJIwgF+uXQNAhCAAAQgAAEIQAACEOhvApKCKkqiSeJPYwyq8Mj09LTNz8+HCEFFCWqf5ooajBGFihxUgRI1pSNr0jEShjpG59y6dStURVbqscYoJKKw3z4vEnyu9bxKsCoMa/w/zf1LvuxpxJlPSW3T5WDZAwKVVlz2ZY8e9AjC1McX1LE0CEAAAiKAJORzAAEIQAACEIAABCAAAQhAoEcJfPDBByE1WOMRSgqeOnUqRBKqSrHGFVT0oKID9/b2QspxFIEqUqIU5CgFFZEoaajtWo7rH330UThfUYV//dd/bbourX8IZKmkoIvh6oZXFt50GbjlacM7LgProdJwo7ruEpBU4f55ozwpBLpLAEnYXf7cHQIQgAAEIAABCEAAAhCAwB0EJPd2d0uhUMm7775ri4uLoTKxoggVTaiIPx2jJhmo9bhNojBGESrlWMcpolDb1SQVNek8HScBKcn4rW/9YThmYoKqpAFUD3zJVCDExwRUIREtp42SNeubQQIqMlD7VFRERURCARIXhi2XwP7F37siChVpSIMABCBwOAJIwsNx4igIQAACEIAABCAAAQhAAAIdI6BIP40dqHRjTYogjKIvRgnqGAnAKAvjw2l/PEbiUMfFbe1zSUK1GI1YqZRDGjKSMJLsxDyO+5enDefvUpIvTxdW0ZC8qMhuHh1Y37ZmbT3IwaTuYwt65WEiBTvxnrgHBIaDAJJwON4zvYQABCAAAQhAAAIQgAAE+oiAxgx89913rFQqhTEIJe4UCSjJFwuUxJRhiSVFBH62SQDmslDnSBa2pyLHqEPNix5lOOrCUBGLus/s7OxnL8XasRFQIZFG5VZIDVakYMuLiySJyz8vLlKrqKjI/nv1d+wr4T8JxLxJJh7bo3FhCEBgCAkgCYfwpdNlCEAAAhCAAAQgAAEIQKC3CUj6Xbt2LaQBRzkoGRgLjmh/eySh1pVCrG35dkWmafpsU/SgpGGMIoyRhplf+5NPPgnjHX72DNYeloCKiZin/CYu/kJFYU8ZTl0AKi1YhUOSuo8d6GnCKizymWIjoaJw6n7QowRpEIAABDpIAEnYQdjcCgIQgAAEIAABCEAAAhCAwGEISPTt7OyECsRR6GlblIG6hmRfbFEQRnmoY9VuT0XWNl0vysK4ruN3d3dDlKK20Q5DwMP4XK62QrSf5mLukX9hsySfKgs3XQZu+ViCO0EKKkpQRUU0xmDDKw4zZuBhOHMMBCDQKQJIwk6R5j4QgAAEIAABCEAAAhCAAAQOSUAFR15//fUwDqGKlkgCxihCRRYqAlDrUfhJDkZBqO1pqojCVogqlAC8myyM23Se7vfWm2/a008/fcgn5LAsqXlkYNnl37aPEehVpsN4gau+rerLu3lRkSAQJQ8lEXOpmJNrX4YlBCAAgd4ggCTsjffAU0AAAhCAAAQgAAEIQAACEDggIKEkeadowRhBKPmnSUIvjikYownjMXGepomfrylPS46iUNeNcvDgZvsLzf105du3D+u6UoBDVWGXgYoWVARgGDcwq3sKccnfi6cJh2hBTwv2tGHJQUnDlqcZSxpmzv9uKd/DypN+QwACvU8ASdj774gnhAAEIAABCEAAAhCAAASGlICEngTf3SIJtT1KwnictmmSHIwpyHFbnH+eKBw+zPeO8lOkYLO6lhcVcTHY8ujAJPFxBUNRkRsh1Xj4eNFjCEBgkAkgCQf57dI3CEAAAhCAAAQgAAEIQKBvCUjqSfQpcrBer4fqxDG9WJGE416VWPPYJAbVdE6c8tTjNEQgapuO0RRFYRSHmg9TU1VhFRVp1rYsafp4gT5mYObyT9slAZs+XmCIHgxFRJyNsoNHfO4p3CE6UKnDNAhAAAIDRgBJOGAvlO5AAAIQgAAEIAABCEAAAv1PQBGCc3NzQfZJ6MXIQIk+iT9tkzDUXC1Kv3ispJ+W4zzuj1JQ14v7YhET3W9iYqL/4QUg6r/LUE8Ddnr53NODVSgk0zZPHdY+CcLUU4fz6sOeKtxS5WEfZ9CloY6lQQACEBgmAkjCYXrb9BUCEIAABCAAAQhAAAIQ6AsCihJ85pln7NatWwdVjmNqsTqgCEIJQ22L0YXtIlD7JAFj9KDmcYrRhDGiUNcrFov2xBNP2OnTp7Xa901jAuayb9sFqxcS8cjARvWWDx1Y8aIiLgV97EA3hX3fTzoAAQhA4CgJIAmPkibXggAEIAABCEAAAhCAAAQgcAQEJAmffPLJkGa8trYWZGCUhJKBURJqLkkYW4welCCMMrBdFmpbFIfty6qY/Pjjj9upU6fipXp63vKoQKUEq7BIK8uj/yQAU58atfVQSKTlkYDaF+aeWqxliUFFEhIl2NOvl4eDAAS6RABJ2CXw3BYCEIAABCAAAQhAAAIQgMC9CEj+Kapveno6pBdL4mlswpgaLPGnJtEXIwnjtbRN+yUMY2pyFIPaHvdFoai5mu43OzsbL9PFufrmqdJeJTikC0vw+eRf8nUXhKosrOhARQuqwnCaln25EiIFgyTc71MXO8GtIQABCPQdASRh370yHhgCEIAABCAAAQhAAAIQGHQCkoKXL1+2N99806rV6kHREgk9Te2RhGIRowy1HCWg5hKGMWJQklHbJA7bpaH263oXL160xcVFXaKrLUslBZteWXjDU4M3fcqLi2gcwaSx62nDHilIqnBX3xE3hwAEBpMAknAw3yu9ggAEIAABCEAAAhCAAAT6mICiAxVFKFH48ssv24cffhgiCWOUoKSgxhGMYxJK8sUmEaimeZwkBjVpXdeIy0pUPn/+vF26dCkIQqU5H3fLXPZlPk6gUoW1rMIhTZeBkoBKF1bacCvL04IlC0PKsPqk9OEQUZj377ifk+tDAAIQGDYCSMJhe+P0FwIQgAAEIAABCEAAAhDoCwISf/Pz80HiraysWK1WC5JPUYCSg+2TxJ/WY+pwjDjUsVrW/igY41zbJ1w0Li0t2YULFw6k46PDUbSjFwUJ1YHzyEdXlgfpwiokknlqcNLcDWIwqW/7+ILrQRwm9T1/ziqRgo/+ErgCBCAAgQcmgCR8YGScAAEIQAACEIAABCAAAQhAoDMEnnrqqZAGXC6X7YMPPrD19fUg+xRpKAGotOQYTahtapJ/ihiMcjCuK3pQy5qrKRLxca9o/Ad/8Af21a9+1SYmJsL2R/2S+RiBjcqtkBqsSMGWpwgniVcUbpasVrn5qQD0Z/GV8J8/2P5tJRMf9Qk4HwIQgAAEHoYAkvBhqHEOBCAAAQhAAAIQgAAEIACBDhBQNOHU1JR96UtfClJPt9zc9IIdHhkY5Z/kYBSF2q/tcZ/WY4pxPEfbTpw4EdKLJQivXLlycG3t+7ymNGAvl+LCz6MBFRGYKLqxlqcHp76sdGEvOJImnkqcuCD0SsKtTOnFvhymmh7w827BPghAAAIQ6BIBJGGXwHNbCEAAAhCAAAQgAAEIQAAC9yMgAahoQY1LKMlXKpVsb2/P6nUv4rGfSqxrtEtCrUdRGMVgFIU6TuMOLi8vh+mVV165iyB0iXePKD9FCbZcAjZVTMSn1FOFk0Rpw15tWEVFaht+rkQiDQIQgAAE+o0AkrDf3hjPCwEIQAACEIAABCAAAQgMJYEXX3zRrl69aj//+c/t+vXr9otf/CKIwiASPeIw3U8xlhCMqceKRJQwVIqxljX+4Ne+9jWTHFQ0oVKO21soKOLRgKkLv8wjA5P6jo8XuOaRgTXfpkIjXlTEi4fkEnJ/3MH2sQcRhO04WYYABCDQVwSQhH31unhYCEAAAhCAAAQgAAEIQGBYCUjoLS4u2nPPPWfnzp2zhYVF293dCVWPq5WKXbt2zco+V/SghKAiBlUdeXJyMkyLi0teCGXGHr+6bAszqY2P7FhtdzVPBfaU4GS/2rCiApVC7PnCLge9CnFSDtGDmdKGE41nSHXhYf0M0m8IQGCwCSAJB/v90jsIQAACEIAABCAAAQhAYIAIKF1Y0YQSgY899pjduHEjpB+vra1Z1asf24an+3rlj7ExjWU4aU8+8ZgtLszbiZMn7MrlS1YcG7Hx0bKnBm9areTjBNZVVMQrCntRkXr1ZhhbcIBw0RUIQAACEHgAAiMeJs6osQ8AjEMhAAEIQAACEIAABCAAAQj0AoEsa7ksTA4Kk9RrZWs26lbeWbFbNz+29bXr9vwz56w47k+beUERF4EqOjIyogrCeRXhlpb9OooOVJERGgQgAIFHIVAoLtiF539kI4WjqZb+KM/CuQ9OgEjCB2fGGRCAAAQgAAEIQAACEIAABDpPwMVey8f8CxWDXfYFqZc1bDQIv8SmxupWNC8gMl6x8t6G3VhZsReemvHIQR+vMC37tBvkIFEinX913BECEIBAPxBAEvbDW+IZIQABCEAAAhCAAAQgAIGhJ6BCImlTqcLbLvyqltQ2rVG95eMEVrzASCmMHZj4mIG3bpXs7//+1/bT//t39vJT/4Utn54fenYAgAAEIACB+xNAEt6fEUdAAAIQgAAEIAABCEAAAhA4dgItjwpsuvhLvYBIK2sGISgBmPqk7drfUjSh7wtzVRn2Za8q4inHniqsiEIaBCAAAQhA4CEJIAkfEhynQQACEIAABCAAAQhAAAIQODyBPMk3pAuH9OD9cQG9yEgYJl6iL/UKw7UNjxQs5RWHk5JXHPY0YZeG9epqkIGHvx9HQgACEIAABB6MAJLwwXhxNAQgAAEIQAACEIAABCAAgQcmkKWK/kusWd2w1NOFmz5ljV1LPTow9Xmj7lWJs9SvmxcUcSMY/gs3Uq1JogQfmDknQAACEIDAgxFAEj4YL46GAAQgAAEIQAACEIAABCBwBwFFAWY+TqCi/rScejRgs+4pwlr2dGGlDbdcAiotuNVyYaiU4SyPJpQ8DGnDrgWPqi0tTNvVyydtrFA4qktyHQhAAAIQGHACSMIBf8F0DwIQgAAEIAABCEAAAhA4CgJKC/ZIvxDRt58iHKL+fNnFnwqJZE0vINLcDWIwqXu0YG09iMOkvhf2a+zATrSxwqgtzU/ZxeVFGxsb7cQtuQcEIAABCAwAgREf/+Lo/lw1AEDoAgQgAAEIQAACEIAABCAAgdsJKDqwUbnl4wXuhkjBls8THzMwbZZ8vMBbQRSGc8I/r/ZThQ/+qRVTiG+/6tGvh3/c+X2baeYRjC2bmCjY6MjI0d+IK0IAAhC4C4FCccEuPP8jGylM3GUvm3qdAJGEvf6GeD4IQAACEIAABCAAAQhA4FgJhAhBS134eTRgiAisWdaqufhL99OFq/l8P5U4pAwrvTirh+1ZUuuZMQODDnQpWBzzNGP+tXesnxsuDgEIQGDQCPBjY9DeKP2BAAQgAAEIQAACEIAABO5CQMU/FGd3Z5RfljZc9jV9DMEtS3xKPVU4SZQ23AiRg01fb3mBkX5o6qGni3kitPrry6OjRhxhP7w5nhECEIBA9wkgCbv/DngCCEAAAhCAAAQgAAEIQOAYCYSCIl44RFWEs7TmInDHxwtc83Tcmm9ToREvKqLiIS7XDsYdbB97sI8qC6sP5UrTSuWaVX1+6eKijSuqkAYBCEAAAhC4DwEk4X0AsRsCEIAABCAAAQhAAAIQ6HUCmYs+jwZ00echf/4/n8KyVxNWWrBSiCUHPV1Y0YGShYoYzDJJQpeHfozv6PVOHur5sqxle5W6rdwq2cZm2ZaX55GEhyLHQRCAAAQggCTkMwABCEAAAhCAAAQgAAEI9DUBCcJG5WaIEAxSsLGTFxVxGVj37ao+PCwt8YIln1zfsld/+aG98daKffHF8zY9OT4s3aefEIAABCDwCASQhI8Aj1MhAAEIQAACEIAABCAAgeMlkPlYgeZRgaoqrErCqUcDpl5VuJU1fVkpxKUQRZj5mIF59KCnDLsUzNOGvfCIFx+hQQACEIAABCBwfwJIwvsz4ggIQAACEIAABCAAAQhA4LgIKD3YU32D2PMKw2GuIiG+PVYR1rakuROEYC4Ky36OJGHZ5aGnELswpEEAAhCAAAQg8GgEkISPxo+zIQABCEAAAhCAAAQgAIFHIKCxAnPZt+1jA1YtqW1ao3rLMi80ktQ9cjApD8x4gY+AiVMhAAEIQAACx04ASXjsiLkBBCAAAQhAAAIQgAAEhpdAy6MCmy7+lCacpwiXgwBMXQJqu/a3QrGRZj5XlWFFBnp0oSIJfWV44T1Ez0dHRmxqsminlmbs4rlFGxsbfYircAoEIAABCAwjASThML51+gwBCEAAAhCAAAQgAIEjIdAKVwnpwpJ5cTIfF7Dl+yT6vHJwUtvwtGCNHVj34QVLnjpcDtKwXl0NxxzJo3CRQMAdYShUcmJx2spn5q1QQBLy0YAABCAAgcMRQBIejhNHQQACEIAABCAAAQhAAAK3EVBRERULaVY3fLzAbWv6lKnAiEcHpj7XessrD5tJIOpkl4f5gi9KIhIleBvSR14dGyvY1ctLdunCokditqxYLDzyNbkABCAAAQgMBwEk4XC8Z3oJAQhAAAIQgAAEIACBByagtF9VDda4gSoekiXVPG3Yi4ZkibZXfXvqYwkqhbgW9meZRwuqurDLQR2vaEJa5wh4IKGNjI6a/48GAQhAAAIQeCACSMIHwsXBEIAABCAAAQhAAAIQGDQCivLbTxsOUX6K8PM+epSfxg3Mml5ApOlFRZK6pfUtLyqy5nJwv6iIz5GAvfV50Ksb8ffpNaPDe5QwlDikQQACEIAABO5HAEl4P0LshwAEIAABCEAAAhCAwIASaPkYgZJ+Sg3OPPIvbaqa8F6oKNyorIaIQKUK5+MLSjvtjzvoSxqHMMjEAWXTr93SuypXmlYq16zq80sXF23cU5BpEIAABCAAgfsRQBLejxD7IQABCEAAAhCAAAQg0IcEVDHYLHHxVw1pwVnT04FbShtOPfjPowI9FTjMveqwCoqokrDWQ7qwzxPfrmhCWn8RSNPM1jb27J0P1uz6yo79zV++bOOzSML+eos8LQQgAIHuEEASdoc7d4UABCAAAQhAAAIQgMAREFBKacgNVmzf/rIu61F/YQzBujU9RTjxKa1vW5LsughseKVhLyri6y0fb5A2WARSL1ayvrlnb71zy954a8X+8nvP29zsxGB1kt5AAAIQgMCxEEASHgtWLgoBCEAAAhCAAAQgAIHjJaCiIRozME8VrrkI3LFmzVOHvYBI2thzAbgfFegSMU8Nbk8VllAkSvB43xBXhwAEIAABCPQXASRhf70vnhYCEIAABCAAAQhAYGgIZGGcwFYrCUKvlWlsQC2neXqwS0JVHVZasKIDJQsVMZhlkoRecMQrE6s6MQ0CEIAABCAAAQgchgCS8DCUOAYCEIAABCAAAQhAAAIdJqBCIo3KzRAhGMYMbOx4urAXFnEZWPftSiemQQACEIAABCAAgaMigCQ8KpJcBwIQgAAEIACBviFQq9WtUqnYRx99GOZbW1v2zjvvWLPpkVdhfDez8fFxe/LJJ21+ft7m5ubC8tTUlBWLxb7pJw/auwRC8RAfD1BjA4aKwh4NmLoAVORf2lQKcSlEEWZ+TB496CnDKiwSKgp74REvPkKDwN0IjI6M2NRk0U4tzdjFc4s2NjZ6t8PYBgEIQAACELiDAJLwDiRsgAAEIAABCEBgUAlIAEoOlstl290t2c2bN8P6xsaGffDBB1av14Mk1HGShBKCCwsLYVpcXAyycHp62mZmZmzE/yFOg8C9CeRFRILUU0mRMP6fi72wWZIvCSnDoaCIIgR9PEFFCcZqw01fJ1X43nTZc28C+tY0PTluJxanrXxm3goFJOG9abEHAhCAAATaCYz4L8H+qwoNAhCAAAQgAAEIDD4BycF/+Id/sBs3btj6+noQgaOjox5pM2aNRsPHcMssTdODiEKJQK1ru6Zz587ZlStX7Ac/+EEQhYNPjB4+LIEsUVGRssu/7XzcQJ83a6u+rerbFDGooiKqLKziIZKIuVTM76dlLfFres6Drw9CQJ8ajV+Zpi3/jLX8jx0F/qjxIAA5FgIQeCQCheKCXXj+RzZSoKr6I4Hs0slEEnYJPLeFAAQgAAEIQKCzBH7+85/brVu37Pr160HInDp1ypQ+LEmoKUmSA0GoiELJwVqtFoShBKL26/ydHY/wcqFz/vx5+9a3vtXZTnC3niHQcsHXrG16arCqCCtFuGyZKg37pO3ar+hB7QtzLzgSIgNVdERjCYa/01NduGde6AA9iGKcR8L3tQHqFF2BAAQgAIGOEEASdgQzN4EABCAAAQhAoFsEJPQUQSjBp0myT3JQacOaK1pQUxSDhUIedaPj2hMutK4xCzX/5JNPQndKpVK4js6hDRKBPIJPqcIhTVipwiFdOEb85dWFk9qGjymosQM9Td1ThRMXhZKG9eqqH8+YgYP0ieinvsRIQg8iDDK6MObf0/qpAzwrBCAAAQh0jQCSsGvouTEEIAABCEAAAsdNQNGAEoR/+7d/exABeOnSpVCMROMKKs1YIlCCUJMkoKIHq1VPCXUZKPmnsQm1TyJR+xRVKEm4ubnp4xru2p//+Z+HNGRFI9IGg4CKgigVuFnd8AIinibsU6YCI75NlYW13vLKwyFVOPhEl4cxNVgRgkEoDgYLetF/BJRivLPj38fqHuGa+DAJyws2TvGS/nuRPDEEIACBLhBAEnYBOreEAAQgAAEIQKAzBFSMREVJJPQmJydtYmLCTp48GQqRSBJKBGqsQQk+SUBJwTguYUxBlkTUJDkoYaj9WlYBlGvXrtlbb70VBOTzzz/fmU5xl0cn4BIvS33MwLTmPs8/Axo/0CMArSWp4mnCShV2CZimSiGuhWNVUERpwooa1DYiBR/9NXCF4yGQJKl9eG3L1jb2rFyp25+dmHFJSFX246HNVSEAAQgMFgEk4WC9T3oDAQhAAAIQgMA+AYm9d999N4xBqGhCVSmen58PknBubi6kCccxByX+NKmporH+ke2jeoXluE/bdU2tK0JR0+rqqr3++uu24UVQnnvuuSAaw0X40gMElCIcwvz2o/wU4eeP5YJQYwOGasLNbZeCPv5kfcsa1TUXgJVQVCTzoiIShTQI9COBxKMHP7m+ZR984n8g2arYH3/jSZuZRhL247vkmSEAAQh0mgCSsNPEuR8EIAABCEAAAsdOQBGCpdJekISqZKyqxBKEmhRRGNOM9SAxgjCmFuvcYjHx7ebpx59GDyoVOYpELavp2LffftvHOly1P/tXf26zs7N+bcYnDHC6+EVRf5J+Sg3OFBHYLLkM3POpbI3KqrtDl8BhvME8NdjVb5CHsoj5vi4+PLeGAAQgAAEIQAACXSKAJOwSeG4LAQhAAAIQgMDxEVCUn8YLlMzTsqSgJolARQNqm+RgjBJsfxJtjy2mIWubljWpxbRkbVfqcb1eCynHU1MSkEjCyO945goHVLqwVw329N+Wqgb75F/2113muiRMQuXh8kHacNqshOrDSWMnCMLjeTauCgEIQAACEIAABPqXAJKwf98dTw4BCEAAAhCAwD0IqPDIu+++E/Yquk+pwlHwKcVYcjCOLxjTh9svNTKiMQpzKSgheLdJslESsujjFEorvvPO7z1ScS6Me9h+LZaPlkBeVMSLzHhRkaS+6dOWVxXecRnoYlBFRWpbpAofLXKuBgEIQAACEIDAkBBAEg7Ji6abEIAABCAAgWEiIBH40UcfhXRgRRAq4k/Rg5J62qdlRQBquySh0objpH2ZV7dt3aVCbYwojCwlD3V84tP7779vL7zwQtzF/CEJKCpQ0X55qnAtjB3YrHnqsBcLSRt7LgBVQMTHDFTkYEgbbk8VztOHH/LWnAaBgSAwOjpiSwvTVq01bGpy3KObqbw+EC+WTkAAAhDoAAEkYQcgcwsIQAACEIAABDpLQDJQFY2jCIwpxhKB2qembVESSvRpysWT0lnzpvW7tSgLNdekc9e9eEm89t3OYVskoFRhrx4cUoRVRMSnsOxy1qMBW6ow7JWGE59ChWGPDlS0YJZJEnrKsBcdUeERGgQgcHcChcKoLS1OKSnf5ud8CARfp0EAAhCAAAQOQwBJeBhKHAMBCEAAAhCAQF8RqFQq9sYbb9jy8rLNzMx8JnJQkYWShZorBTkKxCgKtU/LcbxCze8lCwVFx+qcN7zKsaoo0z6fgARho3IzRAhKCmYeNZgkXljEZWDdt2ucQRoEIPDwBIrjBXvpuXMPfwHOhAAEIACBoSWAJBzaV0/HIQABCEAAAoNPIAo8STxFFapJDGo8wjjOYIwejGJQx0ZRqG1xirLwXsLw7jGHg8+4vYcaL7CVNcLYgKGisEcDpi4AFfmnwiFpoxSiCDM/5rPFRvarDfv5NAhAAAIQgAAEIACB7hBAEnaHO3eFAAQgAAEIQOAYCUTxF6MBo+iL8k8pwjpG+9W0rGPiPJ4Xj9E8Hqfl9u1xXzhgGL74WI1hLEATB/GT4BNDCcIkryzs6cGpIgTreZSgiooohbjp66QKD8OHhD52k4C+WymNPwsLLSt4xfVPa7Z388m4NwQgAAEI9DoBJGGvvyGeDwIQgAAEIACBhyIg0ScpqHEC6/V6SC/WuqSeIgmVbqxoQrUo/XSOZKHO0bLm8RpRMEaZGM+J84d6yD47SRIwaWy7/Nt2GaiiItteTXjVowWrvqyIQRUVUcSm5GEuUx3ufi9lEvuswzwuBPqQQOZ2cGenZtW6R/AmmZ1bXrBxipf04ZvkkSEAAQh0ngCSsPPMuSMEIAABCEAAAsdMYGJiwi5evBgEn2SfUo0lBrUsOSixJ9mn1GNFFapF2aftEoI6VvP25SgINdd+naPzde1Tp06Z7tvfzftc33U2Ne+bRwYmXkjExV8q+RcqC7s8VZVhLyISogZdDqaJj8OYuoxQxWGNJ6iKwzQIQKBrBJIktY+ubdraRtnKlbp9/8SMS8Ji156HG0MAAhCAQP8QQBL2z7viSSEAAQhAAAIQOCSByclJu3Llil2/ft2q1eqBJNTptVrtIJJQ65J8Mf04isLbxaCEoMTg7VO7JLx69arpvr3f7hXl55F/Lvma1bUwpmAm6efCMEl8XMFmyepVFRVBAPb+++UJh51A4tGDH1/ftg8+2bDNrYp9+xtP2sw0knDYPxf0HwIQgMBhCCAJD0OJYyAAAQhAAAIQ6CsC09PT9txzz9nq6qrt7nrVXE83VtSg0ocl9jSPhUtiJKE6GCVhjBTUXMIwysH2yMIYaah9koMvvPBCqKTcq6AkAFVUpFnbsqTpYwX6mIGZyz9VG5YE1PiBeUERjTHoIlHZwSM+DwObedQkgrBXXy3PBQEIQAACEIAABI6EAJLwSDByEQhAAAIQgAAEeolATDeWGJQgjEJQYk9SUCnHShGOUYTtolDHaIoysV0UShLG8QrjcdqvpvTmrqYbu9jLUk//VaqwC8FMqcBeLMRaGpfMqwmrorCEYFoOKcM6VgVFMh2rwiKeRkyqcC99inkWCEAAAhCAAAQg0FkCSMLO8uZuEIAABCAAAQh0gIAE4OnTp4MMlMyTyNO4hFpWi9skD28fl1ByUMdrHqMIdXwsYhKlofZr0vm635kzZ8L8eLunCL+8+off3W+lcD/NFOnnRVZUTbi57cLPpZ9XGG546nCWVkJRkZA+HIqKHO8TcnUIQKDLBHyYVf9biI2MjthoWOjy83B7CEAAAhDoGwJIwr55VTwoBCAAAQhAAAKHJSD5Nzs7ay+++KLNzc3ZG2+8cRAZGIVfeyShRF9sUf5pLiEYpygZtR7TllXy5Lnnn7dz586F+7VHJMbrHdncC4LUyyuWNnYPUoRTjRfohUMalVXvn9KEc7kZpKEqDCtt2C1ivu/InoQLQQACPUxAYnBxftrOnmzYZHHMxgqffn/r4cfm0SAAAQhAoAcIIAl74CXwCBCAAAQgAAEIHD0BCbuzZ88Gyffhhx8eRBLGSseSgEo7VpNU1LpalIRajpGEEoMx+lBztYKLxampKbtw/rydv3AhpC6HHQ/1RfdWurCPmaixA1v55Av76/l2FRVJm+WDtOG0WfHUYY8U9PEFSRV+KPCcBIGBI1BwKbi0OKXvKDY/N4kkHLg3TIcgAAEIHB8BJOHxseXKEIAABCAAAQh0mcCXv/xle+qpp+zatWsmUVgulw8iAyUGoyRsjyTUI0cRGOVgjD6MolDHTHpxlCeefNK+8c1v2gWXhI/SVBRE6cDN6oanBm/6lBcX0ZiBiUcOqtiIxhSkQQACELgfgeJ4wV567tz9DmM/BCAAAQhA4A4CI/7X8vzP5nfsYgMEIAABCEAAAhDofwISfbdu3bJ//Md/tOvXrwdhqF9/FGl4uyTUthhJqHmUhHFZNHTMpUuXQqGS733ve2Hsw2Kx+LmglO6rCsIqJBKKhDRK1nQZKAmYeiRgKCDiRUVURKTlhUY0vmBLEYsaa1BRhb5dkYY0CEAAAhCAAAQg0MsECsUFu/D8j2ykMNHLj8mz3YMAkYT3AMNmCEAAAhCAAAQGg4AiBs97SvDy8nIYS3Bzc9NqtdrBuIKKIpQEbG9RFEoSxmVFEUoGKsVYacwah7A9glAyT1LPv+xfT5IvTxfOXPppLMGkuRuEYFLf9ujAdReGVY8adHGoysNECra/ApYhAIGHJKDvZvojQxYWWlYYK5jGT6VBAAIQgAAE7kcASXg/QuyHAAQgAAEIQGAgCHznO9+xSqVir776qr355pv29ttvhzEHJQnHXCQm++MOSgoqWlBNkYYShZokGx977DF74YUX7JueYjzt6caxKVKwvncjpAYrUrAlIZgocrBk9eot/we7FxUJlYjDv9qlEYNAzM+XTIxXYg4BCEDg0Qhkbgd3dmpWrfsfJ5LMzi0v2PgYxUsejSpnQwACEBgOAqQbD8d7ppcQgAAEIAABCDgBRQPu7OzY1tZWmFZWVkJU4fb2tr3++utWrVbDNDk5GaIGFTF49uwZn07Z6RMztjBbsPnZMZudGfXIHKUQVzxCsBQKjmhMwTyaMBYbyasNSxpiAfn4QQACnSJQrTXt57/6yK7f3Lbd3Zr9l//pV23BC5jQIAABCHSCAOnGnaB8fPcgkvD42HJlCEAAAhCAAAR6jICiBpeWlkIU4IkTJ0wysFIp2/TUpN1cueaFTcatMjHq24shcrDZbNrM1JhdOr9ky6dmrFioW8G8mnCtlI8n6GMMNus7HinY7LGe8jgQgMCwEgiRhC4H1zbKtrnlf8hIGc90WD8L9BsCEIDAgxJAEj4oMY6HAAQgAAEIQKDvCRSLEx4pOGFzc3MeBdiwRm3bvv7KFU/Nq1lS3XLxt+YFTlbs3/xX/4P98D/7A/vm89+2xvaIeTkR73t7qrCW+x4HHYAABCAAAQhAAAIQgIAhCfkQQAACEIAABCAw4ASyfKxAF4AaOzCvJOypwZ4enHgkoKIAM9+XZTUb8SrCo15MZMzKHjFYDqnIadLw1GIvSkIwzoB/TugeBCAAAQhAAAIQGG4CSMLhfv/0HgIQgAAEIDAgBGTw9qsKH1QqziP+Wi7+mpW1XBRq3MC6iors7RcVublfVORODImPNajqxDQIQAACfUXA6y6p9tLI6IiNhoW+enoeFgIQgAAEukgASdhF+NwaAhCAAAQgAIFHIyABqGIhzeqGRwXuuAjcscwrCiuFWJWFEx8vMMsaIYLQbWCeKTzic6/+qdDAvOrwoz0DZ0MAAhDoJQISg4vz03b2ZMMmi2NevZ3Kxr30fngWCEAAAr1MAEnYy2+HZ4MABCDQYwSSJPHCDmWPwnIp4wUd6vV6SMfUY7b2I640xtvY2JiNj4/bzMxMKP6gdRoEHo7AfqVgyUCvJhykoEs/Cb9M2zxVuJU2XRBuhyrDEoNps+yfx2aYJ408nfhB7x0+z+4R5+ambML/kU2DAAQg0C8ECi4Flxan/M8gmc17VWMkYb+8OZ4TAhCAQPcJ8Ftv998BTwABCECgLwhkWWa7uyX73e/esq2tLVtfX7cPP/zQPv744yAIJVU0ffWrX7WFhQU7ffq0Pf/887a4uBiKQ4wo5YkGgQckICmY1Lc9QtAloI8VmNQ2rVG95WMIeoXhuiIGfZxBScMjbolXA1Wq3vNPn7czpxeO+OpcDgIQgMDxESiOF+yl584d3w24MgQgAAEIDCyBEf8HHYPtDOzrpWMQgAAEjobAz372M1tZWbEPPvggXFDCb3R0NEQTNhoNj+jKXOCkYb1YLIZjtK5jtP7ss8/aSy+9FKTh0TwRVxkYAl5IpF5e8SjA3YMU4VTjBSZla1RWXTynHjXoEYT6dcWjB1uqHqK04TD+oPaJxHH8KuNxiy4Kt3ZqNjXpUbHT+ed6YLjTEQhAAAIQgAAEIHAMBArFBbvw/I9spDBxDFfnksdNgEjC4ybM9SEAAQj0MQEJwM1mT6jkAAA/30lEQVTNTdvY2AjRg1qX9JP8UzpxoVAI60o/jpJQy5KGOlYpyUo1vnnzpp06dcqWlpZseXnZB1QnqrCPPxYP8OiSd671fHzAOHagxg9047e/7qnCHinYrK7lKcIaRzAt+3IljxT08QUlCLvTRsLn+9SJme7cnrtCAAIQeEgC+qNKo6E/qrS8MvuI/5we5efuQ7LkNAhAAALDRgBJOGxvnP5CAAIQeAACEoR///d/HwShJOC5c+dscnIyyBOJQm2TFJQQ1LLGKKxWq0EOSgRq0vb33nvPdnZ2QnryD3/4wyAWH+AxOLRPCagoSKvV8IjAdU8N3vRpKxQXaaX1UGm4WdtySXj0qcJ9iovHhgAEIHAkBFIvzLS+sef1mVqhuvHZsz5WcIE/zh0JXC4CAQhAYMAJIAkH/AXTPQhAAAIPSiCPQGjYq6++GqII9/b27MSJE0EOnjx5MkQGRvmnSEEJwlqtFmShBKH2SRxKImqKBU4kCXXcT37yk5B2/Mwzz4T9D/p8HN87BJQKnDY9NThUE66HwiFNl4GSgKmPGai5KgtnqSoQK2pQU54urIhCRRH2apPcbjRTu3Gr5FVCp+zk0nSvPirPBQEIQOAzBGr1pv3LLz/w72GJFcfH7Afffc5mp0n7+wwkViAAAQhA4K4EkIR3xcJGCEAAAsNLQNKvVCqFMQg1V5udnQ2VilWERBIwikRJQK0rvTjKQaUjx2XJQjVdU8sSLx999FEoanLx4sVwXR1L610CeXpwHANQ6cOSfHm6cObST4Iw8bTgEB3oBUaatXWXgl5gpO5RLC4I+zVSMElbVmukdu3Gln+eDUnYux9RngwCELiNQObfvzY2y1ZvJKE6u9ZpEIAABCAAgcMQQBIehhLHQAACEBgiAu+++6795je/sRs3boS0Yo0heP78+VChWJGESimW8KtUKmFZYw6qxbkEopYlDjVp3ELNdZ5koYqfKLrw1q1b9oMf/CDIxyHC21ddVaRgfe9GSA3OPCqw5cVFkqQUxGDdKwwrnVhjDkoaaq7/8mV1UzJR8/5su6Wa3VjZsf/xf/6Z/Zs//4I9fvlkf3aEp4YABCAAAQhAAAIQgMAhCSAJDwmKwyAAAQgMA4FqtWZra2v28ccfB9E3MTERJN7U1JRpWVF/mmIqsQRgnCQHtax9mksUaorb4z4JQhVC0XalMusYXZvWWQItVQgO6cJeJMQj/7Kk5jK3FsRflvqyrys9OGl61eHEBaGnBrcyTx+WLFQase/3DZ196E7ezQWnxvNS2l7iVY5pEIAABCAAAQhAAAIQGHQCSMJBf8P0DwIQgMAhCUjalcvlIPBWV1ft0qVLYRxCCcJYyTimFd8uC9tloJZjBKHEYJSE2q4IREnC7e3tkNK8s7PrgnASSXjId/Tgh8XIvjuj/IL082rCzVpeUCT1VOEk2XUB6KnhHjHY9PV+TRV+cE6cAQEIQGCwCMSf05rTIAABCEAAAoclgCQ8LCmOgwAEIDDgBCT23n//vSDvNAahqhgrwk+RgUoTVpPw07iCca5zPtvyYiWSgzGaUPvbowuDOPTzxvyYd999x6shV2xx8eXPXoa1RyagsQQl+1IfL1CRgUl9x4XgmhcUqfm2vTwq0CMD9S6VVhyiAkNkoNYlF29/t4/8SFwAAhCAAAQ6QKBQGLUzp2ZD8aXiuH4ej3bgrtwCAhCAAAQGgQCScBDeIn2AAAQgcAQEJPyUaqyxBhX1J7EXZWCUhLqNohJ0rGRhLEai9SCW2gaha49ekBjUsTGyIVzbr7XmEYuSkbSHIZDlYwUqLdgln1KAYzpw4hWHlSqs1GClEntusMvBqk9lP863Sw6GisMaU5B2NwKFwkgY8P/0SS/aM1282yFsgwAEINCTBMZdDL7wzLKl/rO54D/LtU6DAAQgAAEIHIYAkvAwlDgGAhCAwBAQkOTb2tryyL5qEIRR8knuSRJqf9wmHNoeZaHmuSiMsvBOYDpXclBTti8g19bXbcajFmn3IqBovhjZF6uA5CnEShduVtZyUSjpV49FRfasXr3pkhABeC+qh9leGBt1gT1mVy6csMX56cOcwjEQgAAEeoKAogefefJMTzwLDwEBCEAAAv1FAEnYX++Lp4UABCBwbAQUGfjWW28FITg3NxckoMYPVFXiGAkoMSjJJ+Gn4zVJDmp7vtwK67kwjFIrjz7Ug+fRhh7Y5ufo2m++8YZHtyXH1qd+vXAYL9DThZvVDS8csuMi0FOGmyWPCmyEysJKHc4yiduYJuxsR1wohmIkLhURhI/86udmJ2x6qmj/7Y/+2CYn+HXpkYFyAQhAAAIQgAAEIACBnifAb709/4p4QAhAAAKdISCBJyEo4adliTxNkn/aphaiAH2bmo6JklDzfDmXhtqnKTZd5/ambYpQlCwcviaRp2rBPpmnCodlH/fRJV8WlpshLThpbvv4gaUgBtOmpwq3mr5cdmmYpxMPH7fO9Xh0xKNe/bekEwtTnbspd4IABCBwBAT087fR8Mh+/2/E/ysW8z/uHcGluQQEIAABCAw4ASThgL9gugcBCEDgQQm0i0HJQYlDycEYLaioQrUoAqMg1Dwe075N14vH3v4s0oifqsTb9w7uuqSgogOT+pbL1aolXmG4Ub3lQwdWfJsiBn2cQY8UpEEAAhCAAAQelECatWx9Y88yl4WjHvl/9uycFwujyvGDcuR4CEAAAsNIAEk4jG+dPkMAAhC4B4EoCBXhJzmopiImapKD2i9hGFuUf4oG1D7NoyiM8ygMtb990rkD2zwNuFH1SsL7BUQU/ZemFU8ZrniF4c08ctDTiVVcpOXRg6pErGUPHwyRhL5hYNH0S8dqjaY1PRJnc6dsC7NTtkhEYb+8Op4TAkNPoFZv2r/88gOvbpxYcXzMfvDd52x2emLouQAAAhCAAATuTwBJeH9GHAEBCPQIAUmldvEk4RSr7kbhVCwWg8SS2JLU0ry92EaPdKUnH0OcxE+iTzxjZKDWoyjUsrjqWB0Tp3b5d/uyrqOm7fE9RQC63/j4eFztk3ku8EJF4TAG4P5YgErsktxTpWFFCtZ8PEFPFVaF4VZS8rEF90KqcL26Go7pk84O7WPWG4mVK01bublro8ujSMKh/STQcQj0H4EsbdnGZtn0fWyiOOY/h/jDU/+9RZ4YAhCAQHcIIAm7w527QgACD0hA8mVvb89u3LgRptXVVdvc3LTXX3/9M+LpxRdftBMnTnhqzVm7cOGCnT9/3mZmZhCFh+At+ffMM8/Y9evXbXd312q1WhCF2q4mURglodajfI3yT3NJXB0TowfbpW6UjjouCsnHHnvMNPVTU1EQjQ3YqKz7eIHbHm22bVlj11JPD059rvWWFxhxLbqfS61RoSQP9/+RJrFI63kCKzd37PrKrv34//i1/avvPGeXLiz2/DPzgBCAAAQgAAEIQAACEHgUAkjCR6HHuRCAQEcIvPbaa7a2tmYffPBBEFcST2qSUQsLC0ESSjxpfWVlJRz7u9/9zqampoIgfPrpp03T1atXw3l8uTsBpRE/9dRTVq1WbX19/aBIiSSh+GquyD/NoyCMV9J+Te0iMMrCKA411zFxruvofhcvXoyX6Ym5IgSVJpyGasL1UDikWfcUYY8ITH3MQM1VWThLPUXYZWFIGfZ++YKvK21Yn09EYE+8zEd4CL3SNM087d6jQn1OgwAEIAABCEAAAhCAwKATQBIO+humfxDoYwKKHozC6ubNmyHCTXJKEW2SVVpWlGCUU9ouAaUUZE3b29vhWMnCkydP2unTp216evoOwdXHiI700cVzcXHRJiYmDiIBtU1MJfTUtKz3ou3tTe9A22MEYXwncbvmsWlZk6Tk0tKSzc/Px10dm0vmSeop1E/P7V982fvggi/zsQElCFVYREIwqXu0YG3dpaAXGKn7QPAuCCkq0rFXxY0gAAEIQOBBCfiP6EJh9GDyAsc0CEAAAhCAwKEIIAkPhYmDIACBbhCQIPznf/5n+/3vfx9koSSfxq+TIIzFMySlJAQlr1RoQ5Mi2LRfc23/zW9+E4ThJ598Yt///veDKOxGf3r9nmJ2+fJle+ONN6xSqRxEEkoIirNEoQSijtO2+A7Ur3YZKOZRFurdaJ/mcZvW4/V0vzNnznQUjSIF63srQQKG8QI9RThJFDm4a3WvMKx0YsnDXBzelip8kELc0UfmZhCAAAQgAIFDEyj4z+kzp2a9cEnqhUsKpnUaBCAAAQhA4DAEkISHocQxEIBAxwl8/PHHtrW1ZYoglJhSNKDGGlS0oCa1KJ/axaDkVYx6izJL+zc2NsI5b775pp06dcquknoceLR/ETuxloyVvFMkpoSftquJq6LuxD+yjedru95HFICa61xNcXuUhzpHEYS6z+zsbJC+8TqPOlelYE8SdeHnlYQ98i9r1ixr1YL4y9OFq77slZg9UjBNfJ9HDmp7K/MUYqUR+zZfedTH4PwBIDDu/7CenCrayaVpm57qt+I6A/AC6AIEIPDQBPT967mnzvpYuT5UiAtCrdMgAAEIQAAChyGAJDwMJY6BAAQ6RiCmrL7//vt269atUJxEkWZKK5bci4IwRqWpuIa2KVJNMkvnS2BprnVNOrZUKoXCJ4qS0xh4miS9ogDrWAd7/EaShCr68uSTT9qvf/3rMAakIjLFM8pXSb/ILc61X5OaZKCWYyRnuzjUuxj396V3qvEIH04S3jvKT+nCKhrSrG16avCWpZ4qnCS7YVuioiK+Tqpwj38Ie+TxVBF0dnrCLiwv2vzsVI88FY8BAQhA4P4EFD34zJOdjdK//1NxBAQgAAEI9AMBJGE/vCWeEQJDREBVdSWnfvvb14PYW14+a5cuXbK5ubkgCSWZJJ+UiiwZJXElKRij3IRK+9WiwNI5atr+q1/9ypR2LLH4xS9+MRQ+CTv5ckBA8m55eTkIQlWRvnbtWhCt4izmSvm+PZJQJ0sMRiGoZXHX8doWxaHe0xMuIF955RX78pe/HCJED258iAWNJSjZl/p4gVlacxG440JwLUQFpo29PCLQowJ1f6UVh6jAz4w9SJTgITBziBM4vzxvZ0/P2eNXT9qkC0MaBCAAAQhAAAIQgAAEBp0Av/UO+humfxDoIwKSSZJ/N27ccEFV9Sdv2eTk5MGksQijbIoRhZprkpBqF4ZRHMZtUWop9VhRhRJfzz77bCiaEWViH6E61keVBFSEn+SslpX2rYhNMRZHyVYxE9v2lou5XA5GSah3qknren9KG7/qqd5KNVZ06J3sXTQq/Xe/sEjLzzVVDHbhl29XUZGyJZ4urIjBVOMJesRglvnzNTzF2FOJlU5Mg8CjEhjzz/eYf8QVUUiDAAQg0E8EMv+Z26in/jPW/Oe2Cr4pc6KfesCzQgACEIBAtwjwm2+3yHNfCEDgDgKSTxJSv/jFL0LKqyrtLiwshChCSasoBiWclF6s1i4JJaEksiSetKzjJKji9igSJQn/5d//+xBJGKv53vEwQ7xB/JR2rCIvErZ7e3um9O9yuRwKw0Q5GMVrOyrxFufIPgpCXVNjSmqsw7/6q7+65ziEkoGNymou/jRGoEcMSgiGoiKVmy4AvSoxDQIQgAAEIACBexJI08xWVnf9d6RRm5oct6XFKSuMULzknsDYAQEIQAACBwSQhAcoWIAABLpJQGLpnXfesevXrweBFCMIJfgkmuKYg+0SSiJKTQIqF1afph1LZGlSJJyiBzXXuTH9telpsB9++GE4XxGFUXyFDXw5IKDxCX/4wx/aL3/5yyAMX3311cBTzBVpJaaKWNBc29TEUu9G0lfvZXp62r75zW/a008/aY8/fsVa9VUXjh4BqJRhF4CZIgJ9rtThLGv4uYoeVKqw/29Ey5o8fRhBePBeWDh+Art7Nf++k1q50rCF+SlbnJ88/ptyBwhAAAJHQEDft/7tT16zxYUpu3xhyf7o6094ASYk4RGg5RIQgAAEBp4AknDgXzEdhED/EFCkWixEItEkwaQmgSjhFOWThFSMVGufR0mlcz4Vh1Eg5kVM2o/R/RRVSLs3ATHXeJAao3B0tGCPPfZ4iCzMMq8g7KK1XKlYxacoCQuFUU/hnvFqihKGqU2Mj7gk9IrJSyM2N1m1YmvTGrVtTw1WdKCmsr/L/RTiMKYgqcL3fhvs6SSB3ZIPTbDXsPXNkl32GyMJO0mfe0EAAo9CIMtatleuW3F8zP+wlxcTe5TrcS4EIAABCAwPASTh8LxregqBniYgybS9vR0ElKIIlUYsQaXIP0UCar8mNYlBiUNNcVveuTyyUMvtMjAKR23TspqusbOzYxsbG+EacXvYyZc7CDz33HP2zDPPeor2y1745ZrL1V1bW1uzd999N0x6RwoknChO2YsvPGZzs5O2NDdmpxYSL/rgsnB0xVq1D231vTxN/I4bsAECPUbgvQ/X7JMbO/b671bsT771lF25uNRjT8jjQAACEIAABCAAAQhA4GgJIAmPlidXgwAEHpKAhN+bb74ZxJ2EXZSAiiCMRTMk9mKL0lD7JRJ1vPbHKR7XPpckjPJQx//+7bdta3PT/vRP/zSkI7cfy/KdBEY89Xd8pGzLJzI7OTtq5xaL9rhXn/7GF8essbfu7DMbLYzY/Nyey9iKi94RGx9tWcEjGlLfN9L2/u68OlsgAAEIQAACEIAABCAAAQhAoJsEkITdpM+9IQCBAwIxsk/pv/Pz80H2SQRGWSi5114oI0pCzaMYjPODi+4vaLtaFIRa1jbdKxY40bbhbjkjFQ7JxwTcHwvQBwYM/LRdYwKmO1YcLdvYeN0mRxKbGS/YqbkZq1c9bVgpyCHasxGiCgv76eKB66d+d7gx03sIQAACEIDAMRPQ7zsaN7jgf6xTdWPLhww+5rtyeQhAAAIQGAQCSMJBeIv0AQIDQkBjBGp8O1UyVnSgJhUsieMUSgjqF19NUQ7qmGYzP7Y9qjBGFgrN3eShtlU9RVZj6gUJNiAMH7YbEnwaG7BZ3QiVhZuNba8svOvSz4uK+FzrLS8wYiZ5qLu4PNRCjA70SEEVeVjf2AuPMDHh8vDkbFjmCwQgAAEIQAACnSNQ8Kj+c8vzHtk/aYtz07ko7NztuRMEIAABCPQxASRhH788Hh0Cg0ZAsk7yL6YP5wKwGURhlH4xmjCKvxhpGOc6X5PW43KUgFpvb/Ea7dsGdtklXprWvJJwNUQEZknVi4bsBTGYJQ1n5VWFUy8gkpZN+8KU1cOxkoNaDxWHPwdQuVK3199eCUecWJpGEn4OK3b1PoGJ4rjNTBVtcXHKJifHe/+BeUIIQAAC+wQmimP21S9c8mwJLz42OxGiCoEDAQhAAAIQOAwBJOFhKHEMBCDQUQJR8kVJqKIYKmQiqSdJqClN8zRjRbRFQRjlYjw/isK4X+ffLg7bU5A72sljuZmi/PbThkOUn26iaD9nlbkA9IjApLHlVYnrlta3rFFdc2lY8cjBknOREHy0oiKVatPeeudW6NnF8wv2yhcvH0svuSgEOkFgZtoF4cKULZ+at1mv0E2DAAQg0C8EJAm/9NKFfnlcnhMCEIAABHqIAJKwh14GjwKBYScwMzPjqcN5IRKlGEvoSQhK7qmYycTERFiPYk8+LArBzNNlo1SM2yQHdb0YMRilofarTU1Nme4Zr9fP/DWWYH3vhkvAHRd/LvwkBJM9jxbc9fECb7kATL17MT34tlThgxTifibAs0PgaAk8/8wZ//7Ssm+88ph//2FAr6Oly9UgAAEIQAACEIAABHqRAJKwF98KzwSBISQgGXjp0iVP65u0jY2NIPeEQWJQ4xLGSELJQh2rJvmnFuWfJKEmScAoCjVvjzCMglDXuHjhgp09e/bgeuFiPfglFBIxLwrS9DRgj/zLmi5QW7Ug/louBFNPBVakYNYs+bLkauKZwYoMrAdhmPk2X+nBnvFIEOhdAoVRH/Q//1bTuw/Jk0EAAhC4C4HU/8BRKtVsxIuWjPvvTZNTYzbq4znTIAABCEAAAvcjgCS8HyH2QwACHSEg+XflypVQbXhtbS2IPUX4KdVYQk8iUE2ST9tj9F97CnGMQoyCUOe0S0Ntj1GFOv/CxYt20acoHTvS0Xve5N5RfqoqrHEBE08RbtY2PVV42/u1m29TURFff9RU4Xs+1gPuiO8lzh/wdA6HQM8QCPG24f+WrfD9hn9g98yr4UEgAIH7ENCQLLfW9mx8fNSmfWzV4sSMjRIRfR9q7IYABCAAARFAEvI5gAAEeoKARN0Fj+yT1FOqsZokXxR4kojap7kEVNwepV8Ug1EKShi2RxhGyRi3ab+iCHtBErZaHgHpsi8NqcI1l4E7LgPXQlRg2vDiIooI1JiBHjmptOIQFRgiA7Uui9EbUYIaIP3s6bnw7pYWpsOcLxDoVwKlvXqo2F2uNGxhfsoW5yf7tSs8NwQgMGQEKtWG/bv/87dhXNXLF5bsj77+hI1NERo9ZB8DugsBCEDgoQggCR8KGydBAALHQWB2dtamp6cPov0k9DRJ/EmGSQzGuaSgWi7OclkWBWAUhvH8OG+PJNS1OjcmoRdMUfqvy0AJvZae3Zcl/PLtLjSbZUs8XVgRg6HAiEcNZlnNlz292FOJlU7c6604XrBzZ3NJqIIPNAj0M4HdUt1Kew1b3yzZZe8IkrCf3ybPDoHhIqDxVPfKdSuOj3lGRv471HARoLcQgAAEIPCwBJCED0uO8yAAgSMlIGmnyL5SqRRkoMSeBGC16uPt+VwRhNp2eyShHiKKwnYZKLGoKW7TPMpGRSIWi8Vwv+Xl5YOoxCPtUNvFJAMbldWQLiwpmHnEoIRgKCpSuekC0OXhADSJwW//J08OQE/oAgTM3vtwzT65sWOv/27F/uRbT9mVi0tggQAEIAABCEAAAhCAwEATQBIO9OulcxDoLwLj4+N28uRJ+8M//EN77bXXbGdnJwhA9UJyUJGAkomabh/zTqIwRhBqrnTiuH77WIVLS0v21a9+NdxL93yUpqrB7enCadMrCiceEeiRf2mz4pGAJY8W1LM0/DiPBvTnDFLQxaHkYV51+FGegHMhAAEIQAACEIAABCAAAQhAAAKPTgBJ+OgMuQIEIHBEBGIKsMYJfO/dd63mUYRJWwRgFIR3k4R6hCgFNY+T5KGiCOO6qiXPzc2FsQiVbqxr3bcpRTiM+xfnGhdQvk+ST0VFXAh6enDS8MnHE0wkCVV12IVh09f7IVX4vgwOcYBnNwXWErj+P68Mewi2h7guh0AAAhCAAAQgcHgC+jk85n9cLYxpDGf/gUxh48PD40gIQAACQ04ASTjkHwC6D4FeIzA/P29f//rXQ1XjTz75xH75y1968YBGkHlKF24XhXp2rUsAtqcca1ktphvHNGNFI77yyit26dKlcA+t369JAiZKD/bCIlni4wZ6JeFmbdWjBV1g1hUxqKIiDb+MxkiMhUTy++cm8X53GJz9Gvfo5uqujTvXycmCnTo5OzidoycQgAAEIACBPiFQ8ErG55bnbX5u0hbnpnNR2CfPzmNCAAIQgEB3CSAJu8ufu0MAArcRCH/9Hhuzr3zlK/bEE08EQfj2229buVwOMlCH65go+LQcmyIGY9pxuzjUssYevHz5sn3nO9+xxcVFG/N7hKbxAqvrHvUXU4TLHg3nxUI8VbhZ28wjBVVkRBGDIUVYy0obVnSiCpFICOZFVOJzDOt8fXPP/vd/+I2dWJyx8/6Pk+/90TPDioJ+DwCBmekJrww6befOzNnczMQA9IguQAACw0Jgeqpof/ndF/x3pVGbKBZCAZNh6Tv9hAAEIACBRyOAJHw0fpwNAQgcEwGJPBUXuXDhgq2srARBWK+rQnCM0stlYbx9lIOaty9r//T0pI8/uGDnz52yUydUQXk8pAJL9IVIwfpmSBMOlYY9VTjRuIJebbheXQ0yMN6D+ecTaDRSu3Fz1yVry2acMQ0C/UxgemrcFuYm7PSpOf88F/u5Kzw7BCAwZATGXA6eOzs3ZL2muxCAAAQgcBQEkIRHQZFrQAACx0Jgenravv/974coQInCn/70p1ar1UIasQqOSAbG8Qb1ADEKUXMVKxkfH7OpqUn74z96xZ64ctLOn5m2+tb/a9UNH0PQ04ebjW33hPupwsE9umDMBxvM+xPGITyWrnFRCECgxwk88+Rp/+NEy772pSsejfNpxHKPPzaPBwEIQAACEIAABCAAgYcmgCR8aHScCAEIdIKAZKAKmWisQjVVPC6VSmHMwr29Pfvkk489JTkfDzCMweMicGpyzMfFm/L5iM3OjNnFpV2bKbgYrI2FgiJKE1bUYJbUiBTsxEvkHhDoQwKFUR/0n9o7ffjmeGQIQCD1YVa2tqr+x1IfI3hi3DMzRsMfUiEDAQhAAAIQuB8BJOH9CLEfAhDoMoHMzp45ZWdOn7Rz587Y1uamrW9s2MbqLVtbX7PN9RUv2ufSzyN+xgotu7g8bScXJ2x+ppVP0yNWnNi20WzbaqUud2XQb+/BVqqiOKKpbazIQe82/RtMAiGueH90A/9E+2d6MPtJryAAgcEjkCSZXb+5Y3Ozk3ZiadrGxieMgOjBe8/0CAIQgMBxEEASHgdVrgkBCBwNAR8zsF6+6anBO55W3LDMU4Qnk107Pem/+J64aZcWmvbCxdMh7Xjl1q79wz+/ZU9cOGUXzk3ZqKcNj3gUUPilmH/cH837uM9VJopjzn7BTi7N2JIXfKBBoJ8JbG1WrO7jbKrNzk74P7YpXtLP75Nnh8AwEdgr1+1/+be/tGeePGNf++Ile/bps1bwn9E0CEAAAhCAwP0I8NPifoTYDwEIHBMBhei0PO23GaoFt1RB2Cf/sl9JWNsTrzC84ZLQKw+7JEzTss8rVmhVPJ24YeOjqU16Ko3axob/1fzGWjhuInxnwwwGMB38Mungr1xcsvn9yIUO3ppbQeDICWxuV6y0pzFLzZY9jBBJeOSIuSAEIHBMBJRdsVuqWqVat0biRdqO6T5cFgIQgAAEBo8AknDw3ik9gkBfEGhl/ktrq2HN6kYQgUl9y6sK74QxAxMVFaltuSTM/4F+mA6tbezZj3/yH+xv/vKL9sTVU4c5hWOOmMCpEzP213/20hFflctBoDsEXnvzul27sRNu/vWvXKVSaHdeA3eFAAQgAAEIQAACEOggASRhB2FzKwgMEwFFBUr2pc2SFwipWFLfcfG3ZqkXC0kbey4AvXCIT6pQ3PK0Yt+QT/73bm0L68MEjL5CAAIQgAAEIAABCEAAAhCAAAS6SABJ2EX43BoC/U1AqcKSfBJ8HhXolfQspAyn+9u9mnCz7FKwHKoIpy4MFS2YZZKEFZ/nacb9zYCnbyeQenpTo5HYqA8EWfDiJWOFPBW8/RiWIQABCEAAAhA4XgIqHjY1VbQJHwZkzMu0MwDL8fLm6hCAAAQGiQCScJDeJn2BQAcJSA42KqsuAfdCZGDmxUUSjxpMm7tWr9x0aejjC9KGioAEoaopzs5MmMYnXJyfGqr+01kIQAACEIBALxAYGxu1i+cW7dTSrE1NFr06O5qwF94LzwABCECgHwggCfvhLfGMEOgwgXy8wP10YVUWbroITLx4iEf/pc1KKCSigiOZjxn4aSShio5onEFFFeYVQTv52DPTE/bSc5dMc1p3CKxvlu0n/9fr9vQTZ2z59Kx95QuXu/Mg3BUCR0BAkrtez7+XTXtEDg0CEIBAvxCY9d+F/vN//SWbnByz2akJkzSkQQACEIAABA5DAEl4GEocA4FBJOBjALY0DqDFudKG/X9B8nmlYZeAqYqJNHzy8QQTSUJPL5YwbPq6hGEvtanJcS9Yctr/Yj7eS481VM/SaKR24+aunT45Z7PTSJWhevkD2Nk5r9LdaOp7pPF9ZQDfL12CwCATkBS8fGFxkLtI3yAAAQhA4JgIIAmPCSyXhUAvE1AqcKL0YB8nMPMxA5P6thcVUepw1ZcVMaiiIqosrH8gx0IibhBDk0ncX+yh2WOXT9p//9/9hU0WkYQ99Fp4FAj0LYGvvHzRvw/mj18YJQqnb18kDw4BCEAAAhCAAAQgcGgCSMJDo+JACPQTgSzIPom+kBKc5JWEVU04C5WFPVXYowKztOb7fdnloAqMeJigpao4rPEEPaKwn1rBi2XMkBLYT6+MZ4VATxMIhXeovdPT74iHgwAE7k4g9b9wbG9XbbxYCH88HR/34iWMS3h3WGyFAAQgAIHPEEASfgYHKxDoJwL3ivLzyD+XfM3aumVeXTjxwiKtulcW9nRhpQrXqyoq0l8C8DBvpeXRjfqlWBE//B58GGLHcIyPiz7qVY1HFHTFGOnHAJhLdpJAFoZk8I+yf0MJ//GZ7iR+7gUBCDwCgSTJ7NrKjmnYhBNL0zY3NmH+t1QaBCAAAQhA4L4EkIT3RcQBEOgtAhKArVbTmtUNjxbcsmZj26MDd12QNbygyG5Yb6X7qcIhLdilYT7YYN6RMA5hb/XpKJ6mVK7b2+/esmeePGvzsxQvOQqmD3qNyeKYXbqwZKcWZ21+hsrGD8qP43uLwOqa/1HFx9lU0ZIZH2NzeoqhDHrrDfE0EIDAvQiU9ur2P/2v/489//RZ+4MvX7EXnj1nBf8ZTYMABCAAAQjcjwA/Le5HiP0Q6DQBl3ghDVjpwEoXViqwRwCai8E08WrCvi0UFUnLYV+WVkNBkczlYUghTmp9lyp8FIjX1kv2v/27/2D/zX/9h0jCowD6ENeYm5v0f4xcthOL00GqPMQlOAUCPUPgzXdu2eZ2xS6eW7JL5xeRhD3zZngQCEDgfgRanl5RrydefCn1PyKHPxXf7xT2QwACEIAABAIBJCEfBAh0hYCnCis/1lse5ZcvuQH0/zVDQZGk6dGBzUqoMNyorrkArOyPM6gxAxUpSGsnsLaxZz/+ya/sb/7yS17l+FT7LpY7REARnK+8fLlDd+M2EDheAr9/b9Wu3fACT17heG5mwi4szx/vDbk6BCAAAQhAAAIQgAAEukwASdjlF8Dth5CAFwSpl296FKALQB8zMG36WIFeNCT1sQMblVV3hz5eYBgLSyLRpaEqDPs86MSwbwiZ0WUIQAACEIAABCAAAQhAAAIQgAAEjpUAkvBY8XLx4SOg6EDXel4lWLIvpAa3VCnY4wX3xxLMi4pseFGRai4KQ9qwhKFHCjZ2/NjBKyoyfJ+D4exxmrasVv//2zu3GEeutI5/7bvdvvW9Z/o2k/ROemeTkBmISCaQYQibh5ANoID2JYIV0iKtYKWV9o3lZZF4QCJvoLyBFIQEUlZiBUQoEvtA9iGKAkxYMptNJslEPX2dbne729122VU23/+4T8eZTNQzm/Kl7H9paqpcLp9z6ncst/2v7/v+NYlFw8bAJByGgwkXEiABEiABEiCBThKA4VJS66nG4xGJ6N9iepZ0kj77IgESIIFgE6BIGOz54+h7jABcgxuNqjEVQXRg9WBNU9WKpmagC1ORyo4RDnts2BwOCfhCAALhjeWCTE9lJaE/TIb1BwoXEiABEiABEiCBzhKIREJaTzUv4yNpSSZixqW9syNgbyRAAiRAAkElQJEwqDPHcXeFAKIDYSICAdAYilT3peYUjAjoafpww5qNIGoQgmEd9QOP0oY1ohBRhFzaQ2A4FZeHvjynhhl0Nm4P4ZNb3bi1L//wg7fka09/RaYmMnLfAmtDnkyNZ/QqgbGRYXHduuRyKSN69+o4OS4SIAESuJ1AWr8Lff23L0giEZF0Mi4QDbmQAAmQAAmQwN0QoEh4N5R4zkARaCA9WFOGVdHTqEBskUIMQxF1D1ZTEVNDUOsIQiR0nV2NDtzS9GLsl4wbMU1FuvN2SSaialgyoXfMo90ZAHvVVGNXPr65I/slR3LZJImQQKAJ5HNJ/UxvSC6tKXsxfl0K9GRy8CQwYAQgCs7P5Afsqnm5JEACJEACfhDgt14/KLKNviGASEGntNY0ElFTkYamCLtqKOKp07BT3lChEPUCrXAIX2K7DwSIGOwbFIG7kLPzY/IXf/qbkohRJAzc5HHAJNCDBH7t0qKoRqj1NRsSGgr34Ag5JBIgARIgARIgARIgARLwlwBFQn95srUeJtCsF+iqOcjeURRgQcXAfRX+EB2oxiGaOgzDkXq9qsGDcBhGujBMR1Bn0NPnHL06qoC9OsXh8BBr4PXq5HBcJBBAAtEIhcEAThuHTAIkoARQKmF1o6jpxlFB6jHSjkNqZsKFBEiABEiABE4i0BGRsK412TzP0z9YrtkihbNarR6PDY9jsZjerQ9JOBzWuhkRs8VjLiRwTwRMirBG9CE9WPdFIPbpvyPBr6EioOfsqDh4qOYim/qeVJFQxT/UGaw5ajCigiGXYBJAWmDV9SSmP+xDIX4R7sYs4gdI1Dgbq5Mip6AbU8A+fSTg6vcWRBJG9LsInEL5nvYRLpsiARJoKwHXq8v6xp5ktWxCWN2N4XJMi+O2ImfjJEACJNA3BNouEkIALBb3ZHV1RddV2d7elkKhINeuXVPhphmVhe358+dlZGREJicnZWZmxqzZbJZuXH3zVmv/hSDqz60WjyIFD47qBW6qIIh6gYgYdEyUoEkLVuXQvP+O3oNNJbH9Y2QP7SNQOqzKz65vyAOLU5JN07ykfaQ/v2VELJyZG5NsJqFGD3Q2/nxSfCYIBFbXtcxE1ZOJMbiDRrUuISMLgzBvHCMJkIBI6cCRv3/lLTl/bkp++eKCpJdOSZi1VfnWIAESIAESuAsCbRUJNzY2ZG1tTW7eXJFSaV8ODg6kUqlIuVzWsPeECjZNYwhEGO7s7JjjEBAhJr733nsyOzsr+XxeFhcX7+JSeEr/E6irAIjIv2ozJVgjAI3wp1tXIwERBYiU4IZXMfsQB+FCjOjBOlyGPXUX1ohCLv1J4NbWvvzTD/9LvvUHv0qRsEtTnFezkl9/YlFmT+XVZZq1Ibs0DezWJwJX31mRwu6hPHbxjEyOp1UkTPnUMpshARIggfYSwI1wR83EqjVPPA2JZrGc9vJm6yRAAiTQTwTaJhIinfjmzZvy9ttvy4cffmhSiZFSjBXL2NiYST+GUFir1eTw8NCIiI6DaC+kiYosLS3J3NyczM/PH7/OPMH/+pgA5v5OUX56TCMFa2V1ElZDEZiJNByYiuybVGGnvK7PUwDs4zfGiZd2a7skr/zLf8vvPntBXY7HTzyfJ/hPIJ9LyJOP3+9/w2yRBLpA4CfXVmV5rajRsaMqesdkNE+RsAvTwC5JgARIgARIgARIgAQ6SKAtIiEEv9dee022trY01bgop0+fNiIfBELUHLTCIMRB1CpEdCHEQUQUog4hjmP/+vXrsr6+bsTDZ599VoaHhzuIhl11kgAEwEZDRcDKjkYDHkpV6wXWazASqaoIuK/pwsVm9CDqDJpVRcOhln0KhJ2cLvZFAiRAAiRAAiRAAiRAAiRAAiRAAiTQZwR8FwmRLgxhcHd314h9EAaRMhyNRo0hCfhBJESkIQRDiIQIiceKwuB4jAWPIRYiNXlzc9OkIKNm4fg4I4QMoMD914wEhBB4bCKiLsIQ/OoQCDVVGGnBbk3NQ9yKioLbKg5qqnADzsMaOVhtphMH7rI5YBIYIAKe15CKU5OYMS8ZMsXSB+jyeakkQAIkQAIk0BME8JsqmYwZw5KIGpfQS6wnpoWDIAESIIFAEPBVJITA98YbbxhBr1QqSS6Xk9HRUSPsQRBElCDEQUQJ2tqEeA2ew2ojCe1jKyZ+8MEH8uqrr8rCwoI899xzpp1A0OUgjwl8YipSNHUC3UpBowU3pK4uwzAVqZs6gp84Xh+/kDskQAKBIQCB8MZyQaansmpcEpFh/YHChQRIgARIgARIoLMEIpGQqQ88PgLjpRiNIDuLn72RAAmQQKAJ+CYSIrX49ddfl+XlZSMETk1NiV0RAWhTjJGKjAhBKxpCGMRzWLAP0RB3v2xUoRUUUdcQzsh4fPnyZZmYmAg0+L4bvBqCOAfrRvRD5B9ShGEa4mntwOrhpokeRNRgw6QK61aOUoVN/UGNHmVF5b57S3T6gjLphPzSI/cJtly6Q2BlvSh/83c/lq8/94icUqHw3P2T3RkIeyUBHwicnspJRG9g4jMlRldQH4iyCRIggU4RyOrn1h/9/uP6GRYy0f2RCN3ZO8We/ZAACZBA0An4IhJCuENaMOoHQgBExCDci7Ei3RipxjgHYiDEPzzfGi0YCiHKEGv9WDzEOXbFa9Duobojr6gZSlmFRrQXifgy/KDPYQfGDwVPZT1NB26mCld16yInXHU/pA/rcZiKVLa1jmC5KRR6B0eCoc5Vtajn0lSkAxM10F2kh+Ny4cEZwZZLdwi4bl2Ke2Vxqq64XvPmT3dGwl5J4IsTmD2dM58nuUxc4ppCz4UESIAEgkIgFBqSXIY3TYMyXxwnCZAACfQSAV9Utv39ktYNvCXvvvuuzM7OmjTjbDYrqVTKiISoL4gFYh/EQSzYQuTDU9g2Bb+GERQhJmKFwGgFQoiCSGG+evWqXLr0hGRzee0na543DfK/thGAa3CjUVVnYa0TqNGB1YO1Zu1AT81mqnvGbKSB+oJcSKCLBBZmR+R733m6iyNg1yRAAv1E4KuXl/rpcngtJEACJEACJEACJEACJHAiAV9Ewhs3PtIowjVJp9MmehCRgxD3bIQh9q3wh3RirHbRp/RcRBaGVIhq1ia0AmJrxCH2VUmUmIqHK6srEolG5OGHHz4WHW173N47AUQHerWSEQAbEP7USbjmFDT4z9Fjh2ZbVxGwaTCigmHd0bWZLmyMSDSKkAsJkAAJkAAJkAAJkAAJkED3CdRcT5ZXdiWjkdAj2aSENd2Y5iXdnxeOgARIgASCQMAXkXBvb08ONBUY4qBNEcbFQxiEIAizEvvYOhnbrXmi5T8Iina1bdkthKmQRiCW9veNg7KNUGx5OXc/h4BJD0bhP1MXEFtEd2ptQBX46uosbGoIah3BuqfGMpo2XKts6X5ZBcOSPq/pxYwU/ByyPNwrBOr1hlT1S3FMvwgjzYZL5wmE9PM7apyN1UmRU9D5CWCPvhJw9fuLfqxIRG9SNr+X+No8GyMBEiCBthFAyY+bq7vGSCydSujvp4b5HGtbh2yYBEiABEigbwj4IhKura1JoVAwKcMm4k/xoIYgxEE8bhXzcBziIaIMP4kqvHPtKisWYmvTlD197frGBsIPTTt9MxNtvBBECjqlNRMpCFORhqYIu2oo4tX2xFGHYaQTq2p4JBxqncHjfQwKEYNtHBybJgGfCJQOq/Kz6xvywOKUZNOsS+gT1ntqJpGIypm5MclqHaREnM7G9wSPJ/ccgdV1/RtZ9WRiDO6gUYnHWJew5yaJAyIBErgjgb29ivz13/6nXPmVL8lvPf2QTE5mVCjk3bs7wuJBEiABEiCBTxHwRSRcWVkxkX2IJIQgaEVAa2ICkQ8LtlYYbBUJEQGE19weXWhfZ0ds24ZBCtrBawZ9aboFI124bKL9kDZcr1eM8Ff3Kmoegv2aioL70nA1ZVgjBZvpwo4+h7WiIiA5Dvr7qB+uf3NrX/7xn9+Sb33jSYqEXZrQvKY0XXliUWam8zKcinZpFOyWBPwhcPX/bkph91Ae+8WzMjmeVpEw5U/DbIUESIAE2kwAN/wrTk2DNlBXvM2dsXkSIAESIIG+IuCLSIhIQpiKTE9Pf0oEdBzHCIMQ9xBRaEVCPLZiIbYQuqwA2EoXx25fIAxuaiRhTaMUB0cktFF+COpDZJ/l0kwXbiBF2NlRofBQaofrKgjuaR1BPQZTEWdXNUCaitz+PuLj/iOwtV2SH/zr/8jvfe2iLJ4Z778LDMAV5XMJufz4/QEYKYdIAicT+MlP12R5rShn5sdU9I7JaJ4i4cnUeAYJkAAJkAAJkAAJkECQCfgiEgIABD1EByJ6EKnB5XLZiHgQAePx+LFIaCMGW0VCpCXjdThmIwxxnj33MxGF6C/I1O9h7KgZ6FaLRvBraGRgzdQL3NTUYdQL1OhANRFBzUCTFqxUjLB6LCJCXLyHzngqCZAACZAACZAACZAACZAACZAACZAACZDAQBLwRSSEMIXVCn8Q+iD8QdzDiucgHCKa0Ap/2OL81i32W0VC227ra+yx/pktveaqin0a+WcMQtRR2Ah/cBnW1GGkCtdxTAXCpgvxwZELMWo74rhrjvcPD14JCZBAUAmgflth50BGR1Jao1Zd6/UznwsJkAAJkAAJkEBnCeDvL+qpZtIJ8/e4s72zNxIgARIggSAT8EUkbE0ltnUIrUgIUQ+RhBAErYmJFfogCGLfCoNWZGwVDq2QaIVCnA/BMRLxZegdmjvU/LtTlJ8e00jBWlmdhNVQBGYiDQemIvuaOlxSU5F1fR6mIlxIgATuhkA4TFHqbji16xzUP/poeVtSw3FJ6g0iTke7SLPdThCAW3fE3Ow0Xmmd6JJ9kAAJkIAvBHCjbmFmVMZHhyUaDZugDV8aZiMkQAIkQAJ9T8AXpW1paUm2trbMijqEEPQg5FmxzwqErZGFIIvjEP0gLEIoxPlYsX/7iuNYIA6eOXNGpqamTB/mYI/+BwGw0VARsLKj0YCHUi1vqhi4b8xDPN26TlGvV41EYBxiVhUNh1r2KRD26MxyWL1IAHfLLzx0xtw178XxDcKYlld25cWXfiTf/+4zcmo6I2Oj6UG4bF5jnxKYnsyam5vp4YT+yPbl61KfkuJlkQAJ9BqBbCYp3/7mZYmpK3syHpGhEJ2Ne22OOB4SIAES6FUCvnzrHRkZMenFm5ubRtyDGAjhz4qCNs0YWyw2BdlGCWJ7+759bKMOW7e5XE5GR0d74K5YMxIQQiBEvrqmBhuTELOvAiEeeyqA1orqLFxRUXBbIwQPVBTU+ouIHKw204l79c3BcZFAkAikNXrtwoMzgi2X7hBw9bN8p6gGSro9uq/TnYGwVxLwgcDs6Zz5PMll4hLXSBwuJEACJBAUAmEVBUdyyaAMl+MkARIgARLoIQK+iIRnz541EX7Xrl07rjtoIwltNCEEwlaREAzwHMQ/GzWIx9bABPs4DrHQnoNjWGdnZ000Ifro5vKJqYhGBMJUpHxLowU3pO4eGlMRHKOzcDdniH0PEoGF2RH53neeHqRL5rWSAAm0kcBXLy+1sXU2TQIkQAIkQAIkQAIkQAK9R8AXkRCiHdKMK5XKsUgIQRACH4Q+6258u0hoowNbxUDUMrSvs4Ihnoc4aI9PT0/L3NzcsejYNqwNT0U/rReoTsIQ/FAn0NO04XpNI2UqBRUAm+nE2MJduBlJWNOoQkTRILqQ1sJtmxs2TAIkQAIkQAIkQAIkQAIk8BkCNdcTlADJaCT0SDYp4YjWJfzMWTxAAiRAAiRAAp8l4ItImEqlBGs0GjU9QNBrTTdGejGi/lqjCXEiREIr/mFrV4iBWPHYnoPz8fpEIiHDw8OmP7T78y9NAQ+OwToSFfx0i7qAxwYjGsGoQp/rFExqsKfCYMNVUxEIhZoq7Gh9QYiBXEiABHqDQL3ekKp+KY7pF+EQa+90ZVLwmYzabeaz+Yt8PHdl9OyUBD5NAD+y9WNFP1PwZg7p+/rTz/MRCZAACfQqAdery83VXZmeyko6lZBQuNEDZZp6lRbHRQIkQAIk0ErAF5EQoh2MRC5duiTvvPOO7O3tHYt/iAxsjSS00YQYhI0kxNaKgjaq0G5xHG3AZTCvtQh/4ZFHBJGE6POLLBAFG42qpghrnUD3QKoHa83agZ6jtQL3jNkIU4W/CGG+lgQ6S2D/wJFr763L+XPTksskOts5ezMEUsmYLC1OGXdjuClyIYEgE7ixXNAsCVfuWxjX4v9qnEa77iBPJ8dOAgNFoLhXlr966T/kN558QJ5/5hH9nZZRoZB3OgbqTcCLJQESIIGfk4AvIiH6hnnJU089ZcTBlZUVWVtbM+KerU14p0hCvM5GCkIMxNKaWoxoREQTQlicn583tQjRB/o6aUGEoEkPVgGwAeFPnYRrGhWIfU9rBmILZ2GkBRvBsO7otuksDCOSZgrxSb3weRIggV4h8LH+oP/zF/9N/vLPfkcePn+6V4Y1UOOYmc7Jn/zhkzJzKisxioQDNff9eLE//Pf/lc1b+/LH33hSxsbSamKiSiEXEiABEiABEiABEiABEuhjAr6JhDG9zY5oQkT5IfJve3vb1CmE6IcFYuDt6caWq00ztlsrFOI1SFtLJpMyOTlp2kYfNhrRuAprerA2rv8g8CGFWFOUVfhDfUCvtm/WulcVt7Kt0YFaX9Arq2BYMgIhIwXtDHBLAsEncFiuyk81khBbLt0hkEpG5Utnx7vTOXslAZ8JrK4X5eZaUSpVmKihHAkXEiABEiABEiABEiABEuhvAr6JhMAE8e7KlSsm3fiVV14RRBRubm6qINeMBoTgZwU+U7PqiK0VB7FFRKGNLsQ5SCteWlqS559/XrLZ7PHrESnolNZMqrCJDNRIQddFvcA9rRe4YaIDVTU8Eg5VRDzeR6cQFI8654YESIAESIAESIAESIAESIAESIAESIAESIAEBpyAryIhWMK8JJPJyKOPPioTExNy48YNef/994+NTJB2DPEPgiDEQKyti007xnkL86dlbDQjDy5NSNhbkWppXRyTLlxWEVBTkTVSEFGCJm3YRbqwphAjjditqAjIu/6tXLlPAiRAAu0m4FQ9KewcyOhISiKRkIT1xhEXEiABEiABEiCBzhLA398JLZOQSSfM3+PO9s7eSIAESIAEgkzAd5EQMJB6fPHiRcnn8yZVeGVlVVOPK0YYxB8tCIS23iBEQkQXon4VxMNGqGF+WMYTYTm3eFqmJnLylftz4h5clxrShmEq4uyqBsiUwiC/8Th2EmgHgTCNBdqB9a7brDg1+Wh52xiXJPXznNNx1+h4Yg8SGFKXdDql9+DEcEgkQAInEsCNuoWZURkfHdYAjuZvrBNfxBNIgARIgARIQAm0RSS0ZOfm5kydwvPnz5sahTs7O1IoFHTdlqtXr0qlAmOShgqEQ1rHKie5bFxyqYZk1Lg4kxqSkdyWRCMF2dv++Cgy8CjykFGCFjG3JEACRwRwt/zCQ2fMXXNC6Q6B5ZVdefGlH8n3v/uMnJrOaCR4ujsDYa8k4AOBuVN5icciktBam2H9wc2FBEiABIJCIJtJyre/eVkDN8KSjEcENz24kAAJkAAJkMDdEGirSIjUY6yIFsQWBiRY0+m0HB4eqkioKcL6XEL/eJ2dH9Ef91FJJxsynBRJJ4YkHg+Z6MK7uRCeQwIkMNgExqey8thjRRmfOifx9MkO6INNqz1XH4p5srtXlaH4pESSYzoPufZ0xFZJoAMEzn35gkzuVSQ/vijD6bh+J4l2oFd2QQIkQAL+EEhl/WmHrZAACZDAvRIIRzTqa4g3WO+VW6+cP6Qi3aeLAvbKyDgOEiABEiCBQBF488035YUXXpCXX35ZFhYW5NSpU4EaPwdLAiRAAiRAAiRAAiRAAiRAAoNMgCLhIM8+r50ESIAEfCRQrVbl1q1bMj4+roXSIwIDKi4kQAIkQAIkQAIkQAIkQAIkQALBIECRMBjzxFGSAAmQAAmQAAmQAAmQAAmQAAmQAAmQAAmQQNsIMFG8bWjZMAmQAAmQAAmQAAmQAAmQAAmQAAmQAAmQAAkEgwBFwmDME0dJAiRAAiRAAiRAAiRAAiRAAiRAAiRAAiRAAm0jQJGwbWjZMAmQAAmQAAmQAAmQAAmQAAmQAAmQAAmQAAkEgwBFwmDME0dJAiRAAiRAAiRAAiRAAiRAAiRAAiRAAiRAAm0jQJGwbWjZMAmQAAmQAAmQAAmQAAmQAAmQAAmQAAmQAAkEgwBFwmDME0dJAiRAAiRAAiRAAiRAAiRAAiRAAiRAAiRAAm0j8P/wO0u3f9y8agAAAABJRU5ErkJggg==",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(image_path_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p>\n",
    "<figure>\n",
    "  <figcaption>   \n",
    "<strong>Figure 5:</strong> <em> Figurative illustration of\n",
    "Galileo's ramp experiment setup used for exploring the relationship\n",
    "between time and the distance an object falls due to gravity. To perform\n",
    "this experiment he repeatedly rolled a ball down a ramp and timed\n",
    "how long it took to get $\\frac{1}{4}$,$\\frac{1}{2}$, $\\frac{2}{3}$,\n",
    "$\\frac{3}{4}$, and all the way down the ramp.  </em>  </figcaption> \n",
    "</figure>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    " Why didn't Galileo simply drop the ball from some height and time how long it took to reach certain distances to the ground?  Because no reliable way to measure time yet existed (he had to use a [water clock](https://en.wikipedia.org/wiki/Water_clock) for these experiments)!   Galileo was the one who set humanity on the route towards its first reliable time-piece in his studies of the [pendulum](http://galileo.rice.edu/sci/instruments/pendulum.html)\n",
    " \n",
    "Data from a ([modern reenactment](Straulino, S, \"Reconstruction of Galileo Galilei's experiment: the inclined plane\", Physics Education 43, 3 2008, pp. 316.)) of these experiments (averaged over 30 trials), results in the 6 data points shown below.  Here the input axis is the number seconds while the output is the portion of the ramp traveled by the ball during the experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BwcHBSg9xOM2bNy+nnXZarrvuuiTJwMBAWlpacuGFF2bp0qXPWn/jjTfmk5/8ZLZt23bQt/bt6elJQ0NDdu3alfr6+kOaHwAAYF9G2h2F+rpmX19fNm7cmAULFgxtq66uzoIFC7J+/fp9HvO1r30t8+fPz/nnn5+pU6fmVa96Va644oqUy+WxGhsAAOCwKdTXNXfu3JlyuZypU6cO2z516tRs27Ztn8f88Ic/zLe+9a2cffbZufvuu/PII4/kD/7gD9Lf358VK1bs85je3t709vYO/dzT03P43gQAAMAhKNSZvIMxMDCQKVOm5Kabbsrs2bOzePHi/Mmf/EluvPHG/R6zcuXKNDQ0DL1aWlrGcGIAAID9K1TknXDCCampqcmOHTuGbd+xY0caGxv3ecyJJ56YV77ylampqRnaduqpp6ZUKqWvr2+fxyxbtiy7du0aej322GOH700AAAAcgkJF3sSJEzN79uysWbNmaNvAwEDWrFmT+fPn7/OYtra2PPLIIxkYGBja9vDDD+fEE0/MxIkT93lMbW1t6uvrh70AAACOBIWKvCTp7OzMzTffnM997nN56KGH8v73vz979uzJkiVLkiTnnHNOli1bNrT+/e9/f5588slcdNFFefjhh/P1r389V1xxRc4///xKvQUAAICD9rwj7xvf+Eaqqqoyffr0/a558sknM2XKlEyePDmPPPLIIQ34fC1evDhXXXVVli9fnpkzZ2bz5s1ZvXr10M1YHn300fzkJz8ZWt/S0pJvfvObeeCBB/Ka17wmH/jAB3LRRRft83ELAAAAR7rn/Zy8np6eHH/88RkYGMiTTz65z4eGv+c978lnPvOZXHbZZfnIRz5yuGY9YnlOHgAAMNpG7Tl59fX1mTFjRgYHB/f57Lm1a9fmM5/5TE499dR86EMfer6/HgAAgENwUNfkvf71r0+S3H///cO29/b25vd///dTVVWVv/qrv9rvjUsAAAAYHYc18i6//PI8/PDDWbJkSc4444xDnw4AAIDn5Xlfk5ckO3fuzJQpU/KCF7wgTz31VGpqarJ169bMmjUrDQ0N2bZtW44//vjRmPeI5Jo8AABgtI3aNXnJzx46fuqpp+bpp5/Ov/7rv2ZwcDC///u/n76+vlx99dXjKvAAAACOJMcc7IGvf/3rs3Xr1tx///154IEH8p3vfCcdHR1597vffTjnAwAA4Hk46Ieh//y6vDvvvDMf/vCHU1tbmxtuuOGwDQYAAMDzd0hn8pJkzZo1SZJLL700v/Irv3J4pgIAAOCgHPSZvObm5rz85S9Pkpx88slZunTpYRsKAACAg3PQkdfb25tnnnkmSTwTDwAA4Ahx0JF35ZVX5tFHH82SJUvya7/2a4dzJgAAAA7SQV2Tt27dulx++eVpamrK1VdffbhnAgA4KvT396empialUinbt29Pc3NzGhsbUy6XM2HChEqPB4xTIz6T9+CDD+Z3f/d3s2jRonR0dCRJbrvtthx33HGjNhwAwJGqr68vW7ZsSUdHR5qbmzN37tw0Nzeno6MjW7ZsSV9fX6VHBMapEUfeN77xjdxyyy359re/nba2tnzzm9/MGWecMZqzAQAckfr7+7N169a0tbVl7dq1w/atXbs2bW1t2bp1a/r7+yszIDCuVQ0ODg5WeoijXU9PTxoaGrJr167U19dXehwAYJQNDAyko6PjWYH3f7W3t+fee+9NdfVB3wIBYJiRdod/6wAAPE+lUumAgZck9913X0ql0tgMBPB/iDwAgOdp+/btI1rX3d09ypMAPJvIAwB4npqbm0e0rqmpaZQnAXg2kQcA8Dw1NjbmzDPPPOCa9vb2NDY2js1AAP+HyAMAeJ7K5XKuueaa1NXV7XN/XV1dVq1alXK5PMaTAYg8AIDnbcKECWltbU1XV1fa29uH7Wtvb09XV1daW1s9EB2oiGMqPQAAwNFo4sSJmT59eu69996USqV0d3enqakpjY2NKZfLAg+oGJEHAHCQfh5yTU1Nw26y4tl4QCX5NxAAAECBiDwAAIACEXkAAAAFIvIAAAAKROQBAAAUiMgDAAAoEJEHAABQICIPAACgQEQeAABAgYg8AACAAhF5AAAABVLIyLv++uszbdq0TJo0KfPmzcuGDRtGdNxtt92WqqqqnHXWWaM7IAAAwCgpXOTdfvvt6ezszIoVK7Jp06bMmDEjCxcuzOOPP37A4/7jP/4jf/RHf5QzzjhjjCYFAAA4/AoXeatWrcp5552XJUuWpLW1NTfeeGPq6ury6U9/er/HlMvlnH322bn00kvz8pe/fAynBQAAOLwKFXl9fX3ZuHFjFixYMLSturo6CxYsyPr16/d73J/+6Z9mypQpee973zsWYwIAAIyaYyo9wOG0c+fOlMvlTJ06ddj2qVOnZtu2bfs85jvf+U5uueWWbN68ecR/p7e3N729vUM/9/T0HNS8AAAAh1uhzuQ9X7t378673/3u3HzzzTnhhBNGfNzKlSvT0NAw9GppaRnFKQEAAEauUGfyTjjhhNTU1GTHjh3Dtu/YsSONjY3PWv/v//7v+Y//+I8sWrRoaNvAwECS5JhjjskPfvCDvOIVr3jWccuWLUtnZ+fQzz09PUIPAAA4IhQq8iZOnJjZs2dnzZo1Q49BGBgYyJo1a3LBBRc8a/0pp5yS73//+8O2feQjH8nu3bvz53/+5/sNt9ra2tTW1h72+QEAAA5VoSIvSTo7O3Puuedmzpw5mTt3bq699trs2bMnS5YsSZKcc845aW5uzsqVKzNp0qS86lWvGnb8sccemyTP2g4AAHA0KFzkLV68OE888USWL1+eUqmUmTNnZvXq1UM3Y3n00UdTXT2uL0UEAAAKrGpwcHCw0kMc7Xp6etLQ0JBdu3alvr6+0uMAAAAFNNLucEoLAACgQEQeAABAgYg8AACAAhF5AAAABSLyAAAACkTkAQAAFIjIAwAAKBCRBwAAUCAiDwAAoEBEHgAAQIGIPAAAgAIReQAAAAUi8gAAAApE5AEAABSIyAMAACgQkQcAAFAgIg8AAKBARB4AAECBiDwAAIACEXkAAAAFIvIAAAAKROQBAAAUyDGVHgAA+Jn+/v7U1NSkVCpl+/btaW5uTmNjY8rlciZMmFDp8QA4SjiTBwBHgL6+vmzZsiUdHR1pbm7O3Llz09zcnI6OjmzZsiV9fX2VHhGAo4TIA4AK6+/vz9atW9PW1pa1a9cO27d27dq0tbVl69at6e/vr8yAABxVRB4AVFhNTU0uvvji7N27d5/79+7dm87OztTU1IzxZAAcjUQeAFRYqVR61hm8X3TfffelVCqNzUAAHNVEHgBU2Pbt20e0rru7e5QnAaAIRB4AVFhzc/OI1jU1NY3yJAAUgcgDgAprbGzMmWeeecA17e3taWxsHJuBADiqiTwAqLByuZxrrrkmdXV1+9xfV1eXVatWpVwuj/FkAByNRB4AVNiECRPS2tqarq6utLe3D9vX3t6erq6utLa2eiA6ACNyTKUHAACSiRMnZvr06bn33ntTKpXS3d2dpqamNDY2plwuCzwARkzkAcAR4uch19TUNOwmK9XVvngDwMgV8n81rr/++kybNi2TJk3KvHnzsmHDhv2uvfnmm3PGGWfkuOOOy3HHHZcFCxYccD0AAMCRrHCRd/vtt6ezszMrVqzIpk2bMmPGjCxcuDCPP/74PtevXbs273jHO3Lfffdl/fr1aWlpyRvf+MYRP7MIAADgSFI1ODg4WOkhDqd58+bltNNOy3XXXZckGRgYSEtLSy688MIsXbr0OY8vl8s57rjjct111+Wcc84Z0d/s6elJQ0NDdu3alfr6+kOaHwAAYF9G2h2FOpPX19eXjRs3ZsGCBUPbqqurs2DBgqxfv35Ev2Pv3r3p7+/P8ccfP1pjAgAAjJpC3Xhl586dKZfLmTp16rDtU6dOzbZt20b0Oz784Q+nqalpWCj+ot7e3vT29g793NPTc3ADAwAAHGaFOpN3qD7xiU/ktttuy5133plJkybtd93KlSvT0NAw9GppaRnDKQEAAPavUJF3wgknpKamJjt27Bi2fceOHWlsbDzgsVdddVU+8YlP5B/+4R/ymte85oBrly1bll27dg29HnvssUOeHQAA4HAoVORNnDgxs2fPzpo1a4a2DQwMZM2aNZk/f/5+j/uzP/uzXHbZZVm9enXmzJnznH+ntrY29fX1w14AAABHgkJdk5cknZ2dOffcczNnzpzMnTs31157bfbs2ZMlS5YkSc4555w0Nzdn5cqVSZIrr7wyy5cvz6233ppp06alVColSV74whfmhS98YcXeBwAAwMEoXOQtXrw4TzzxRJYvX55SqZSZM2dm9erVQzdjefTRR1Nd/f9PYN5www3p6+vLb/3Wbw37PStWrMjHPvaxsRwdAADgkBXuOXmV4Dl5AADAaBuXz8kDAAAY70QeAABAgYg8AACAAhF5AAAABSLyAAAACkTkAQAAFIjIAwAAKBCRBwAAUCAiDwAAoEBEHgAAQIGIPAAAgAIReQAAAAUi8gAAAApE5AEAABSIyAMAACgQkQcAAFAgIg8AAKBARB4AAECBiDwAAIACEXkAAAAFIvIAAAAKROQBAAAUiMgDAAAoEJEHAABQICIPAACgQEQeAABAgYg8AACAAhF5AAAABSLyAAAACkTkAQAAFIjIAwAAKBCRBwAAUCAiDwAAoEBEHgAAQIEUMvKuv/76TJs2LZMmTcq8efOyYcOGA66/4447csopp2TSpEl59atfnbvvvnuMJuVI0N/fn4GBgXR3d+eBBx5Id3d3BgYG0t/fX+nRAADgeStc5N1+++3p7OzMihUrsmnTpsyYMSMLFy7M448/vs/1999/f97xjnfkve99b773ve/lrLPOyllnnZUHH3xwjCenEvr6+rJly5Z0dHSkubk5c+fOTXNzczo6OrJly5b09fVVekQAAHheqgYHBwcrPcThNG/evJx22mm57rrrkiQDAwNpaWnJhRdemKVLlz5r/eLFi7Nnz57cddddQ9te97rXZebMmbnxxhtH9Dd7enrS0NCQXbt2pb6+/vC8EUZdf39/tmzZkra2tuzdu/dZ++vq6tLV1ZXp06dnwoQJFZgQAAD+v5F2R6HO5PX19WXjxo1ZsGDB0Lbq6uosWLAg69ev3+cx69evH7Y+SRYuXLjf9RRHTU1NLr744n0GXpLs3bs3nZ2dqampGePJAADg4BUq8nbu3JlyuZypU6cO2z516tSUSqV9HlMqlZ7X+iTp7e1NT0/PsBdHn1KplLVr1x5wzX333XfAzwIAABxpChV5Y2XlypVpaGgYerW0tFR6JA7C9u3bR7Suu7t7lCcBAIDDp1CRd8IJJ6SmpiY7duwYtn3Hjh1pbGzc5zGNjY3Pa32SLFu2LLt27Rp6PfbYY4c+PGOuubl5ROuamppGeRIAADh8ChV5EydOzOzZs7NmzZqhbQMDA1mzZk3mz5+/z2Pmz58/bH2S3HPPPftdnyS1tbWpr68f9uLo09jYmDPPPPOAa9rb2w8Y/AAAcKQpVOQlSWdnZ26++eZ87nOfy0MPPZT3v//92bNnT5YsWZIkOeecc7Js2bKh9RdddFFWr16dq6++Otu2bcvHPvaxfPe7380FF1xQqbfAGCmXy7nmmmtSV1e3z/11dXVZtWpVyuXyGE8GAAAHr3CRt3jx4lx11VVZvnx5Zs6cmc2bN2f16tVDN1d59NFH85Of/GRo/emnn55bb701N910U2bMmJEvfelL+cpXvpJXvepVlXoLjJEJEyaktbU1XV1daW9vH7avvb09XV1daW1t9fgEAACOKoV7Tl4leE7e0a2/vz81NTUplUrp7u5OU1NTGhsbUy6XBR4AAEeMkXbHMWM4ExyRfh5yTU1Nw26yUl1duBPdAACMA/5fLAAAQIGIPAAAgAIReQAAAAUi8gAAAApE5AEAABSIyAMAACgQkQcAAFAgIg8AAKBARB4AAECBiDwAAIACEXkAAAAFIvIAAAAKROQBAAAUiMgDAAAoEJEHAABQICIPAACgQEQeAABAgYg8AACAAhF5AAAABSLyAAAACkTkAQAAFIjIAwAAKBCRBwAAUCAiDwAAoEBEHgAAQIGIPAAAgAIReQAAAAUi8gAAAApE5AEAABSIyAMAACgQkQcAAFAgIg8AAKBARB4AAECBFCrynnzyyZx99tmpr6/Psccem/e+9715+umnD7j+wgsvzMknn5zJkyfnZS97WT7wgQ9k165dYzg1AADA4VOoyDv77LOzZcuW3HPPPbnrrruybt26/N7v/d5+13d3d6e7uztXXXVVHnzwwXz2s5/N6tWr8973vncMpwYAADh8qgYHBwcrPcTh8NBDD6W1tTUPPPBA5syZkyRZvXp13vzmN+c///M/09TUNKLfc8cdd+Rd73pX9uzZk2OOOWZEx/T09KShoSG7du1KfX39Qb8HAACA/RlpdxTmTN769etz7LHHDgVekixYsCDV1dX553/+5xH/np//BzbSwAMAADiSFKZkSqVSpkyZMmzbMccck+OPPz6lUmlEv2Pnzp257LLLDvgVzyTp7e1Nb2/v0M8/v4avp6fneU4NAAAwMj/vjef6MuYRH3lLly7NlVdeecA1Dz300CH/nZ6enrzlLW9Ja2trPvaxjx1w7cqVK3PppZc+a3tLS8shzwEAAHAgu3fvTkNDw373H/HX5D3xxBP5r//6rwOuefnLX57Pf/7z+cM//MP89Kc/Hdr+zDPPZNKkSbnjjjvym7/5m/s9fvfu3Vm4cGHq6upy1113ZdKkSQf8e794Jm9gYCBPPvlkXvziF6eqqmqE74wjTU9PT1paWvLYY4+5tpIx5/NHpfjsUUk+f1TK0frZGxwczO7du9PU1JTq6v1feXfEn8l7yUtekpe85CXPuW7+/Pl56qmnsnHjxsyePTtJ8q1vfSsDAwOZN2/efo/r6enJwoULU1tbm6997WvPGXhJUltbm9ra2mHbjj322Oc8jqNDfX39UfUPO8Xi80el+OxRST5/VMrR+Nk70Bm8nyvMjVdOPfXU/Pqv/3rOO++8bNiwIV1dXbngggvy9re/fejOmtu3b88pp5ySDRs2JPlZ4L3xjW/Mnj17csstt6SnpyelUimlUinlcrmSbwcAAOCgHPFn8p6PL3zhC7ngggvS0dGR6urqvPWtb81f/MVfDO3v7+/PD37wg+zduzdJsmnTpqE7b/7yL//ysN/1ox/9KNOmTRuz2QEAAA6HQkXe8ccfn1tvvXW/+6dNmzbsTjRnnnnmc96ZhvGjtrY2K1aseNZXcWEs+PxRKT57VJLPH5VS9M/eEX/jFQAAAEauMNfkAQAAIPIAAAAKReQBAAAUiMiD/3X99ddn2rRpmTRpUubNmzf0qA0YLStXrsxpp52WF73oRZkyZUrOOuus/OAHP6j0WIxDn/jEJ1JVVZUPfvCDlR6FcWL79u1517velRe/+MWZPHlyXv3qV+e73/1upcdiHCiXy/noRz+ak046KZMnT84rXvGKXHbZZYW7GaPIgyS33357Ojs7s2LFimzatCkzZszIwoUL8/jjj1d6NArs29/+ds4///z80z/9U+6555709/cPPbsTxsoDDzyQv/qrv8prXvOaSo/COPHTn/40bW1tmTBhQr7xjW9k69atufrqq3PcccdVejTGgSuvvDI33HBDrrvuujz00EO58sor82d/9mf5y7/8y0qPdli5uyYkmTdvXk477bRcd911SZKBgYG0tLTkwgsvzNKlSys8HePFE088kSlTpuTb3/52Xv/611d6HMaBp59+Oq997WvzqU99Kh//+Mczc+bMXHvttZUei4JbunRpurq68o//+I+VHoVx6Dd+4zcyderU3HLLLUPb3vrWt2by5Mn5/Oc/X8HJDi9n8hj3+vr6snHjxixYsGBoW3V1dRYsWJD169dXcDLGm127diX52TM/YSycf/75ectb3jLs338w2r72ta9lzpw5+e3f/u1MmTIls2bNys0331zpsRgnTj/99KxZsyYPP/xwkuRf/uVf8p3vfCdvetObKjzZ4VWoh6HDwdi5c2fK5XKmTp06bPvUqVOzbdu2Ck3FeDMwMJAPfvCDaWtry6te9apKj8M4cNttt2XTpk154IEHKj0K48wPf/jD3HDDDens7Mwll1ySBx54IB/4wAcyceLEnHvuuZUej4JbunRpenp6csopp6SmpiblcjmXX355zj777EqPdliJPIAjwPnnn58HH3ww3/nOdyo9CuPAY489losuuij33HNPJk2aVOlxGGcGBgYyZ86cXHHFFUmSWbNm5cEHH8yNN94o8hh1f/u3f5svfOELufXWWzN9+vRs3rw5H/zgB9PU1FSoz5/IY9w74YQTUlNTkx07dgzbvmPHjjQ2NlZoKsaTCy64IHfddVfWrVuXl770pZUeh3Fg48aNefzxx/Pa1752aFu5XM66dety3XXXpbe3NzU1NRWckCI78cQT09raOmzbqaeemr/7u7+r0ESMJ3/8x3+cpUuX5u1vf3uS5NWvfnV+/OMfZ+XKlYWKPNfkMe5NnDgxs2fPzpo1a4a2DQwMZM2aNZk/f34FJ6PoBgcHc8EFF+TOO+/Mt771rZx00kmVHolxoqOjI9///vezefPmodecOXNy9tlnZ/PmzQKPUdXW1vasx8U8/PDD+aVf+qUKTcR4snfv3lRXD0+gmpqaDAwMVGii0eFMHiTp7OzMueeemzlz5mTu3Lm59tprs2fPnixZsqTSo1Fg559/fm699dZ89atfzYte9KKUSqUkSUNDQyZPnlzh6SiyF73oRc+69vMFL3hBXvziF7smlFF38cUX5/TTT88VV1yRt73tbdmwYUNuuumm3HTTTZUejXFg0aJFufzyy/Oyl70s06dPz/e+972sWrUq73nPeyo92mHlEQrwv6677rp88pOfTKlUysyZM/MXf/EXmTdvXqXHosCqqqr2uf0zn/lMfud3fmdsh2HcO/PMMz1CgTFz1113ZdmyZfm3f/u3nHTSSens7Mx5551X6bEYB3bv3p2PfvSjufPOO/P444+nqakp73jHO7J8+fJMnDix0uMdNiIPAACgQFyTBwAAUCAiDwAAoEBEHgAAQIGIPAAAgAIReQAAAAUi8gAAAApE5AEAABSIyAMAACgQkQcAAFAgIg8AAKBARB4AAECBiDwAAIACEXkAMAY+/vGPp6qqKq973ev2uX/p0qWpqqrKzJkz89Of/nSMpwOgSKoGBwcHKz0EABTdf//3f+eVr3xl/vM//zNf+tKX8ta3vnVo38qVK3PJJZfk5JNPzrp16zJlypQKTgrA0c6ZPAAYA5MnT87ll1+eJPmTP/mTPPPMM0mSG264IZdccklOOumkrFmzRuABcMicyQOAMTI4OJg5c+Zk06ZNufHGG/PCF74w7373u9PU1JR//Md/zEknnVTpEQEoAJEHAGNo7dq1aW9vz3HHHZfdu3fnuOOOy7p163LKKadUejQACkLkAcAYa2try/33358XvehFWbduXWbOnFnpkQAoENfkAcAY+sxnPpP169cnSXp7e1NfX1/hiQAoGpEHAGPkjjvuyHnnnZfjjz8+ixcvTl9fXz784Q9XeiwACsbXNQFgDNx9990566yzMnny5HzrW9/KK17xirziFa/Ik08+ma6urpx++umVHhGAgnAmDwBG2be//e381m/9Vo455pj8/d//fWbPnp1jjz02l1xySZKks7OzwhMCUCTO5AHAKNqwYUMWLFiQ3t7efPWrX82v//qvD+3r7e3NySefnB//+Mf54he/mLe//e0VnBSAonAmDwBGyfe///286U1vyt69e/OFL3xhWOAlSW1tbS677LIkybJly9Lb21uJMQEoGGfyAAAACsSZPAAAgAIReQAAAAUi8gAAAApE5AEAABSIyAMAACgQkQcAAFAgIg8AAKBARB4AAECBiDwAAIACEXkAAAAFIvIAAAAKROQBAAAUiMgDAAAokP8HoCUUMhhGbokAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load data\n",
    "data = np.loadtxt(data_path_3,delimiter = ',')\n",
    "\n",
    "# get input/output pairs\n",
    "x = data[:-1,:]\n",
    "y = data[-1:,:] \n",
    "\n",
    "# plot dataset\n",
    "demo = section_10_2_helpers.RegressionVisualizer(data)\n",
    "demo.plot_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The data here certainly displays a nonlinear relationship and by viewing it - and using his physical intuition Galileo - intuited a *quadratic* relationship.  Or in our jargon that for some $w_0$, $w_1$, and $w_2$ the modeling function \n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}(x,\\Theta) = w_0 + xw_1 + x^2w_2\n",
    "\\end{equation}\n",
    "\n",
    "provides the correct sort of nonlinearity to explain this data (albeit when the parameters are tuned correctly).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Notice here how we have two *unparameterized* feature transformations: the identity $f_1(x) = x$ and the quadratic term $f_2(x) = x^2$, and so we may write the above equivalently as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}(x,\\Theta) = w_0 + f_1(x)\\,w_1 + f_2(x)\\,w_2\n",
    "\\end{equation}\n",
    "\n",
    "which clearly shows how we are seeking out a proper linear relationship in the transformed feature space (which in this case is two-dimensional).  Note here - unlike the previous examples - neither of these feature transformations are *fixed* in that they take in no internal weights."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After standard-normalizing the input of this dataset we minimize the Least Squares cost via gradient descent, and plot the corresponding best nonlinear fit on the original data (left panel below) as well as corresponding linear fit on the feature transformed data (right panel below).  Notice that since we have two features in this instance our linear fit is in a space one dimension higher than the original input space defined by $x$.  In other words, the transformed feature space here has *two* inputs: one defined by each of the two features $f_1$ and $f_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameters for our two runs of gradient descent\n",
    "w = 0.1*np.random.randn(3,1);\n",
    "max_its = 50; alpha_choice = 10**(-1);\n",
    "\n",
    "# feature transform \n",
    "def feature_transforms(x):\n",
    "    # calculate feature transform\n",
    "    f = np.array([(x.flatten()**d) for d in range(1,3)])   \n",
    "    return f\n",
    "\n",
    "# run on original data\n",
    "run1 = section_10_2_helpers.BaseSetup(x,y,feature_transforms,'least_squares',normalize = 'standard')\n",
    "run1.fit(w=w,alpha_choice = alpha_choice,max_its=max_its)\n",
    "\n",
    "# plot data and fit in original and feature transformed space\n",
    "ind = np.argmin(run1.cost_history)\n",
    "w_best = run1.weight_history[ind]\n",
    "demo.plot_fit_and_feature_space(w_best,run1.model,run1.feature_transforms,normalizer = run1.normalizer,view = [25,100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Notice that trend is true more generally speaking: the more feature transforms we use the higher the up we go in terms of the dimensions of our transformed feature space / linear fit!  In general if our original input has dimension $N$ - and is written as $\\mathbf{x}$ - and we use a `model` function that employs $B$ nonlinear feature transformations as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x},\\Theta\\right) = w_0 + f_1\\left(\\mathbf{x}\\right){w}_{1} +  f_2\\left(\\mathbf{x}\\right){w}_{2} + \\cdots + f_B\\left(\\mathbf{x}\\right)w_B\n",
    "\\end{equation}\n",
    "\n",
    "then our original space has $N$ dimensional input, while our transformed feature space is $B$ dimensional.  Note here that the set of all weights $\\omega$ contains not only the weights $w_1,\\,w_2,...,w_B$ from the linear combination, but also any features's internal parameters as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##  Implementing nonlinear regression in `Python`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we show a universal way to implement the generic nonlinear model shown in equation (6) above, generalizing our original linear implementation from [Section 5.1.3](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_2_Least.html).   In particular we implement the compact form given in equation (8)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# an implementation of our model employing a nonlinear feature transformation\n",
    "def model(x,w):    \n",
    "    # feature transformation \n",
    "    f = feature_transforms(x,w[0])\n",
    "    \n",
    "    # compute linear combination and return\n",
    "    a = w[1][0] + np.dot(f.T,w[1][1:])\n",
    "    return a.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here our generic set of engineered feature transformations are implemented in the `Python` function `feature_transforms`.  Here we have implemented this function as generically as possible, to encompass the case where our desired feature transformations have internal parameters.  Here we package the model weights in the set $\\Theta$ as `w`, which is a list containing the *internal weights* of  `feature_transforms` in its first entry `w[0]`, and the weights in the final linear combination of the model stored in second etnry `w[1]`).\n",
    "\n",
    "e.g., the `feature_transforms` function employed in Example 2 above can be implemented as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the feature transformation from Example 2 \n",
    "def feature_transforms(x,w):\n",
    "    # calculate feature transform\n",
    "    f = np.sin(w[0] + np.dot(x.T,w[1:])).T\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "If our desired feature transformations do not have internal parameters we can either leave the parameter input to this function empty, or implement the model above slightly differently by computing our set of feature transformations as\n",
    "\n",
    "\n",
    "                                f = feature_transforms(x)\n",
    "                        \n",
    "                        \n",
    "and computing the linear combination of these transformed features in line 7 as\n",
    "\n",
    "\n",
    "                                a = w[0] + np.dot(f.T,w[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In either case, in order to successfully perform nonlinear regression we can focus our attention solely on implementing the function `feature_transforms` - employing the `autograd`'-wrapped `numpy` library if we wish to employ automatic differentiation (see [Section 3.5](https://jermwatt.github.io/machine_learning_refined/notes/3_First_order_methods/3_5_Automatic.html)).  Since only our implemented `model` needs adjusting, nothing about how we implement our *regression cost functions* changes from the originnal context of linear regression detailed in Chapter 5.  In other words, once we have implemented a given set of feature transformations correctly, employing the `model` above we can then tune the parameters of our nonlinear regression precisely as we have done in Chapter 5 employing any regression cost function and local optimization scheme."
   ]
  }
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